TSTP Solution File: SWV697-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV697-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 21:14:28 EDT 2022
% Result : Timeout 300.08s 300.38s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15 % Problem : SWV697-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.16 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.37 % Computer : n025.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 600
% 0.14/0.37 % DateTime : Wed Jun 15 10:44:55 EDT 2022
% 0.14/0.37 % CPUTime :
% 1.52/1.80 ============================== Prover9 ===============================
% 1.52/1.80 Prover9 (32) version 2009-11A, November 2009.
% 1.52/1.80 Process 20177 was started by sandbox on n025.cluster.edu,
% 1.52/1.80 Wed Jun 15 10:44:56 2022
% 1.52/1.80 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_20019_n025.cluster.edu".
% 1.52/1.80 ============================== end of head ===========================
% 1.52/1.80
% 1.52/1.80 ============================== INPUT =================================
% 1.52/1.80
% 1.52/1.80 % Reading from file /tmp/Prover9_20019_n025.cluster.edu
% 1.52/1.80
% 1.52/1.80 set(prolog_style_variables).
% 1.52/1.80 set(auto2).
% 1.52/1.80 % set(auto2) -> set(auto).
% 1.52/1.80 % set(auto) -> set(auto_inference).
% 1.52/1.80 % set(auto) -> set(auto_setup).
% 1.52/1.80 % set(auto_setup) -> set(predicate_elim).
% 1.52/1.80 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.52/1.80 % set(auto) -> set(auto_limits).
% 1.52/1.80 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.52/1.80 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.52/1.80 % set(auto) -> set(auto_denials).
% 1.52/1.80 % set(auto) -> set(auto_process).
% 1.52/1.80 % set(auto2) -> assign(new_constants, 1).
% 1.52/1.80 % set(auto2) -> assign(fold_denial_max, 3).
% 1.52/1.80 % set(auto2) -> assign(max_weight, "200.000").
% 1.52/1.80 % set(auto2) -> assign(max_hours, 1).
% 1.52/1.80 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.52/1.80 % set(auto2) -> assign(max_seconds, 0).
% 1.52/1.80 % set(auto2) -> assign(max_minutes, 5).
% 1.52/1.80 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.52/1.80 % set(auto2) -> set(sort_initial_sos).
% 1.52/1.80 % set(auto2) -> assign(sos_limit, -1).
% 1.52/1.80 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.52/1.80 % set(auto2) -> assign(max_megs, 400).
% 1.52/1.80 % set(auto2) -> assign(stats, some).
% 1.52/1.80 % set(auto2) -> clear(echo_input).
% 1.52/1.80 % set(auto2) -> set(quiet).
% 1.52/1.80 % set(auto2) -> clear(print_initial_clauses).
% 1.52/1.80 % set(auto2) -> clear(print_given).
% 1.52/1.80 assign(lrs_ticks,-1).
% 1.52/1.80 assign(sos_limit,10000).
% 1.52/1.80 assign(order,kbo).
% 1.52/1.80 set(lex_order_vars).
% 1.52/1.80 clear(print_given).
% 1.52/1.80
% 1.52/1.80 % formulas(sos). % not echoed (1355 formulas)
% 1.52/1.80
% 1.52/1.80 ============================== end of input ==========================
% 1.52/1.80
% 1.52/1.80 % From the command line: assign(max_seconds, 300).
% 1.52/1.80
% 1.52/1.80 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.52/1.80
% 1.52/1.80 % Formulas that are not ordinary clauses:
% 1.52/1.80
% 1.52/1.80 ============================== end of process non-clausal formulas ===
% 1.52/1.80
% 1.52/1.80 ============================== PROCESS INITIAL CLAUSES ===============
% 1.52/1.80
% 1.52/1.80 ============================== PREDICATE ELIMINATION =================
% 1.52/1.80 1 class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) # label(axiom). [assumption].
% 1.52/1.80 2 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,A)),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_eq__divide__eq__number__of1_4) # label(axiom). [assumption].
% 1.52/1.80 3 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(C,c_HOL_Ozero__class_Ozero(A),A) = c_Int_Onumber__class_Onumber__of(B,A) # label(cls_divide__eq__eq__number__of_2) # label(axiom). [assumption].
% 1.52/1.80 4 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) != c_Int_Onumber__class_Onumber__of(C,A) | c_Int_Onumber__class_Onumber__of(C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of_1) # label(axiom). [assumption].
% 1.52/1.80 5 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),C,A) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_3) # label(axiom). [assumption].
% 1.52/1.80 6 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | B = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq_3) # label(axiom). [assumption].
% 1.52/1.80 7 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),B,A) = C # label(cls_divide__eq__imp_0) # label(axiom). [assumption].
% 1.52/1.80 8 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),B,A) # label(cls_eq__divide__imp_0) # label(axiom). [assumption].
% 1.52/1.80 9 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Odivide(B,C,A)),c_HOL_Oinverse__class_Odivide(D,E,A)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E),A) # label(cls_mult__frac__frac_0) # label(axiom). [assumption].
% 1.52/1.80 10 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(C,A)),c_Int_Onumber__class_Onumber__of(C,A),A) = B | c_Int_Onumber__class_Onumber__of(C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of1_3) # label(axiom). [assumption].
% 1.52/1.80 11 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | B = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(C,A)),c_Int_Onumber__class_Onumber__of(C,A),A) | c_Int_Onumber__class_Onumber__of(C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq__number__of1_3) # label(axiom). [assumption].
% 1.52/1.80 12 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(B,C,A),A) = c_HOL_Oinverse__class_Odivide(C,B,A) # label(cls_inverse__divide_0) # label(axiom). [assumption].
% 1.52/1.80 13 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Oinverse__class_Odivide(C,c_HOL_Ozero__class_Ozero(A),A) | c_Int_Onumber__class_Onumber__of(B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq__number__of_1) # label(axiom). [assumption].
% 1.52/1.80 14 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | c_Int_Onumber__class_Onumber__of(B,A) = c_HOL_Oinverse__class_Odivide(C,c_HOL_Ozero__class_Ozero(A),A) # label(cls_eq__divide__eq__number__of_2) # label(axiom). [assumption].
% 1.52/1.80 15 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Oinverse__class_Odivide(C,c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_eq__divide__eq__number__of1_2) # label(axiom). [assumption].
% 1.52/1.80 16 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Oinverse(B,A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A) # label(cls_inverse__eq__divide_0) # label(axiom). [assumption].
% 1.52/1.80 17 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber__ring(A) | c_HOL_Oinverse__class_Oinverse(B,A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A) # label(cls_class__fieldgb_Oinverse__divide_0) # label(axiom). [assumption].
% 1.52/1.80 18 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A)),C) # label(cls_power__one__over_0) # label(axiom). [assumption].
% 1.52/1.80 19 -class_Ring__and__Field_Ofield(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(B,C,A),A) = c_HOL_Oinverse__class_Odivide(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__minus__divide__right_0) # label(axiom). [assumption].
% 1.52/1.80 20 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,C,A) != c_HOL_Oone__class_Oone(A) | C = c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_right__inverse__eq_0) # label(axiom). [assumption].
% 1.52/1.80 21 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(B,C,A),A) = c_HOL_Oinverse__class_Odivide(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_minus__divide__right_0) # label(axiom). [assumption].
% 1.52/1.80 22 -class_Ring__and__Field_Ofield(A) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(B,C,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(B,A),C,A) # label(cls_minus__divide__left_0) # label(axiom). [assumption].
% 1.52/1.80 23 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Oinverse__class_Odivide(C,D,A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D) = C | D = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq__number__of_0) # label(axiom). [assumption].
% 1.52/1.80 24 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Oinverse(B,A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__eq__divide_0) # label(axiom). [assumption].
% 1.52/1.80 25 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Oinverse(B,A)),B) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_field__inverse_0) # label(axiom). [assumption].
% 1.52/1.80 26 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(B,B,A) = c_HOL_Oone__class_Oone(A) # label(cls_right__inverse__eq_1) # label(axiom). [assumption].
% 1.52/1.80 27 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self_0) # label(axiom). [assumption].
% 1.52/1.80 28 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(B,B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self__if_1) # label(axiom). [assumption].
% 1.52/1.80 29 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Oinverse__class_Odivide(B,C,A) # label(cls_minus__divide__divide_0) # label(axiom). [assumption].
% 1.52/1.80 30 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),E),C)),A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),E),A)),C) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__divides__special_0) # label(axiom). [assumption].
% 1.52/1.80 31 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__zero__left_0) # label(axiom). [assumption].
% 1.52/1.80 32 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_1) # label(axiom). [assumption].
% 1.52/1.80 33 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__zero_0) # label(axiom). [assumption].
% 1.52/1.80 34 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Oone__class_Oone(A) | B = c_HOL_Oone__class_Oone(A) # label(cls_inverse__eq__1__iff_0) # label(axiom). [assumption].
% 1.52/1.80 35 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | c_Int_Onumber__class_Onumber__of(B,A) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C),C,A) # label(cls_eq__divide__eq__number__of_4) # label(axiom). [assumption].
% 1.52/1.80 36 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oinverse__class_Oinverse(B,A)),c_HOL_Oinverse__class_Oinverse(C,A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),c_HOL_Oinverse__class_Oinverse(B,A))),c_HOL_Oinverse__class_Oinverse(C,A)) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__add_0) # label(axiom). [assumption].
% 1.52/1.80 37 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oinverse__class_Odivide(B,C,A)),D) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)),C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__frac__num_0) # label(axiom). [assumption].
% 1.52/1.80 38 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oinverse__class_Odivide(C,D,A)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),D,A) | D = c_HOL_Ozero__class_Ozero(A) # label(cls_add__num__frac_0) # label(axiom). [assumption].
% 1.52/1.80 39 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Ouminus__class_Ouminus(C,A),A) = c_HOL_Oinverse__class_Odivide(B,C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__minus__divide__divide_0) # label(axiom). [assumption].
% 1.52/1.80 40 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Oone__class_Oone(A),A) = B # label(cls_divide__1_0) # label(axiom). [assumption].
% 1.52/1.80 41 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self__if_0) # label(axiom). [assumption].
% 1.52/1.80 42 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Oinverse(B,A)),c_HOL_Oinverse__class_Oinverse(C,A)) # label(cls_inverse__mult__distrib_0) # label(axiom). [assumption].
% 1.52/1.80 43 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C),C,A) = c_Int_Onumber__class_Onumber__of(B,A) # label(cls_divide__eq__eq__number__of_4) # label(axiom). [assumption].
% 1.52/1.80 44 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) = c_HOL_Oinverse__class_Odivide(B,D,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__divide__mult__cancel__right_0) # label(axiom). [assumption].
% 1.52/1.80 45 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) = c_HOL_Oinverse__class_Odivide(C,D,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__divide__mult__cancel__left_0) # label(axiom). [assumption].
% 1.52/1.80 46 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Odivide(B,C,A)),D) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),C,A) # label(cls_mult__frac__num_0) # label(axiom). [assumption].
% 1.52/1.80 47 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oinverse__class_Odivide(B,D,A)),c_HOL_Oinverse__class_Odivide(C,D,A)) # label(cls_add__divide__distrib_0) # label(axiom). [assumption].
% 1.52/1.80 48 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber__ring(A) | c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(c_Int_OPls,A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__Numeral0_0) # label(axiom). [assumption].
% 1.52/1.80 49 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Oinverse__class_Odivide(B,C,A)),D) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D),A) # label(cls_power__divide_0) # label(axiom). [assumption].
% 1.52/1.80 50 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C),C,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq__number__of_3) # label(axiom). [assumption].
% 1.52/1.80 51 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | B = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(C,A),A)),c_Int_Onumber__class_Onumber__of(C,A)) | c_Int_Onumber__class_Onumber__of(C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of1_0) # label(axiom). [assumption].
% 1.52/1.80 52 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(C,A),A)),c_Int_Onumber__class_Onumber__of(C,A)) = B | c_Int_Onumber__class_Onumber__of(C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq__number__of1_0) # label(axiom). [assumption].
% 1.52/1.80 53 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B),B,A) # label(cls_eq__divide__eq_4) # label(axiom). [assumption].
% 1.52/1.80 54 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C),C,A) = c_Int_Onumber__class_Onumber__of(B,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of_3) # label(axiom). [assumption].
% 1.52/1.80 55 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oinverse__class_Odivide(B,C,A)),c_HOL_Oinverse__class_Odivide(D,E,A)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E),A) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__frac__eq_0) # label(axiom). [assumption].
% 1.52/1.80 56 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | B = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Odivide(B,C,A)),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_0) # label(axiom). [assumption].
% 1.52/1.80 57 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Odivide(B,C,A)),C) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq_0) # label(axiom). [assumption].
% 1.52/1.80 58 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(A),A) = c_HOL_Oone__class_Oone(A) # label(cls_inverse__eq__1__iff_1) # label(axiom). [assumption].
% 1.52/1.80 59 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,A)),c_Int_Onumber__class_Onumber__of(B,A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of1_4) # label(axiom). [assumption].
% 1.52/1.80 60 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(C,c_Int_Onumber__class_Onumber__of(B,A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of1_1) # label(axiom). [assumption].
% 1.52/1.80 61 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_HOL_Oinverse__class_Odivide(B,C,A) != c_Int_Onumber__class_Onumber__of(D,A) | B = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(D,A)),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of_0) # label(axiom). [assumption].
% 1.52/1.80 62 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,C,A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oinverse__class_Oinverse(C,A)) # label(cls_divide__inverse_0) # label(axiom). [assumption].
% 1.52/1.80 63 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber__ring(A) | c_HOL_Oinverse__class_Odivide(B,C,A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oinverse__class_Oinverse(C,A)) # label(cls_class__fieldgb_Odivide__inverse_0) # label(axiom). [assumption].
% 1.52/1.80 64 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber(A) | c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(B,A),A) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_inverse__eq__divide__number__of_0) # label(axiom). [assumption].
% 1.52/1.80 65 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Oinverse__class_Odivide(B,C,A)),D) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__power__divide_0) # label(axiom). [assumption].
% 1.52/1.80 66 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ozero__class_Ozero(A) = c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_eq__divide__eq_2) # label(axiom). [assumption].
% 1.52/1.80 67 -class_Ring__and__Field_Ofield(A) | c_HOL_Oinverse__class_Odivide(B,C,A) != c_HOL_Oinverse__class_Odivide(D,E,A) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C) # label(cls_frac__eq__eq_0) # label(axiom). [assumption].
% 1.52/1.80 68 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E) | C = c_HOL_Ozero__class_Ozero(A) | E = c_HOL_Ozero__class_Ozero(A) | c_HOL_Oinverse__class_Odivide(B,E,A) = c_HOL_Oinverse__class_Odivide(D,C,A) # label(cls_frac__eq__eq_1) # label(axiom). [assumption].
% 1.52/1.80 69 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_4) # label(axiom). [assumption].
% 1.52/1.80 70 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber__ring(A) | c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),A),A) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),A) # label(cls_inverse__numeral__1_0) # label(axiom). [assumption].
% 1.52/1.80 71 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber__ring(A) | c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),A),A) = B # label(cls_divide__Numeral1_0) # label(axiom). [assumption].
% 1.52/1.80 72 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber__ring(A) | c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),A),A) = B # label(cls_divide__numeral__1_0) # label(axiom). [assumption].
% 1.52/1.80 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(1,a,2,a)].
% 1.52/1.80 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex). [resolve(1,a,3,a)].
% 1.52/1.80 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,4,a)].
% 1.52/1.80 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),B,tc_Complex_Ocomplex) = A | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,5,a)].
% 1.52/1.80 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | A = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),B,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,6,a)].
% 1.52/1.80 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A),A,tc_Complex_Ocomplex) = B. [resolve(1,a,7,a)].
% 1.52/1.80 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A),A,tc_Complex_Ocomplex). [resolve(1,a,8,a)].
% 1.52/1.80 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex)),c_HOL_Oinverse__class_Odivide(C,D,tc_Complex_Ocomplex)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D),tc_Complex_Ocomplex). [resolve(1,a,9,a)].
% 1.52/1.80 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(B,A,tc_Complex_Ocomplex). [resolve(1,a,12,a)].
% 1.52/1.80 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,13,a)].
% 1.52/1.80 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(1,a,14,a)].
% 1.52/1.80 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(1,a,15,a)].
% 1.52/1.80 Derived: c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(1,a,16,a)].
% 1.52/1.80 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex)),B). [resolve(1,a,18,a)].
% 1.52/1.80 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(A,c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,19,a)].
% 1.52/1.80 Derived: c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(1,a,20,a)].
% 1.52/1.80 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(A,c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(1,a,21,a)].
% 1.52/1.80 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex). [resolve(1,a,22,a)].
% 1.52/1.80 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(B,C,tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)),C) = B | C = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,23,a)].
% 1.52/1.80 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex)),A) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,25,a)].
% 1.52/1.80 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(A,A,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(1,a,26,a)].
% 1.52/1.80 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex). [resolve(1,a,29,a)].
% 1.52/1.80 Derived: c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),D),B)),tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),D),tc_Complex_Ocomplex)),B) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,30,a)].
% 1.52/1.80 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,31,a)].
% 1.52/1.80 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,32,a)].
% 1.52/1.80 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | A = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(1,a,34,a)].
% 1.52/1.80 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)),B),B,tc_Complex_Ocomplex). [resolve(1,a,35,a)].
% 1.52/1.80 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex)),c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex))),c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex)) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,36,a)].
% 1.52/1.80 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex)),C) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)),B,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,37,a)].
% 1.52/1.80 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Oinverse__class_Odivide(B,C,tc_Complex_Ocomplex)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),C,tc_Complex_Ocomplex) | C = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,38,a)].
% 1.52/1.80 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,39,a)].
% 1.52/1.80 Derived: c_HOL_Oinverse__class_Odivide(A,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(1,a,40,a)].
% 1.52/1.80 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex)),c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex)). [resolve(1,a,42,a)].
% 1.52/1.80 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)),B),B,tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex). [resolve(1,a,43,a)].
% 1.52/1.80 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(A,C,tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,44,a)].
% 1.52/1.80 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(B,C,tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,45,a)].
% 1.52/1.81 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex)),C) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),B,tc_Complex_Ocomplex). [resolve(1,a,46,a)].
% 1.52/1.81 Derived: c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B),C,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(A,C,tc_Complex_Ocomplex)),c_HOL_Oinverse__class_Odivide(B,C,tc_Complex_Ocomplex)). [resolve(1,a,47,a)].
% 1.52/1.81 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(A,c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,48,a)].
% 1.52/1.81 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex)),C) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),C),tc_Complex_Ocomplex). [resolve(1,a,49,a)].
% 1.52/1.81 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | A = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(A,c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex)) | c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,51,a)].
% 1.52/1.81 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(A,c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex),tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex)) = A | c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,52,a)].
% 1.52/1.81 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A),A,tc_Complex_Ocomplex). [resolve(1,a,53,a)].
% 1.52/1.81 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex)),c_HOL_Oinverse__class_Odivide(C,D,tc_Complex_Ocomplex)) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D),tc_Complex_Ocomplex) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,55,a)].
% 1.52/1.81 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | A = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex)),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,56,a)].
% 1.52/1.81 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex)),B) = A | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,57,a)].
% 1.52/1.81 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(1,a,58,a)].
% 1.57/1.88 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,59,a)].
% 1.57/1.88 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,60,a)].
% 1.57/1.88 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex) != c_Int_Onumber__class_Onumber__of(C,tc_Complex_Ocomplex) | A = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(C,tc_Complex_Ocomplex)),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,61,a)].
% 1.57/1.88 Derived: c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex)). [resolve(1,a,62,a)].
% 1.57/1.88 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex)),C) = c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),C),tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,65,a)].
% 1.57/1.88 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(1,a,66,a)].
% 1.57/1.88 Derived: c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Odivide(C,D,tc_Complex_Ocomplex) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B). [resolve(1,a,67,a)].
% 1.57/1.88 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(A,D,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(C,B,tc_Complex_Ocomplex). [resolve(1,a,68,a)].
% 1.57/1.88 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A),A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(1,a,69,a)].
% 1.57/1.88 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_Complex_Ocomplex). [resolve(1,a,70,a)].
% 1.57/1.88 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Odivide(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(1,a,71,a)].
% 1.57/1.88 73 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 1.57/1.88 74 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_zero__less__mult__pos2_0) # label(axiom). [assumption].
% 1.57/1.88 75 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A) # label(cls_zero__less__mult__pos_0) # label(axiom). [assumption].
% 1.57/1.88 76 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__pos__pos_0) # label(axiom). [assumption].
% 1.57/1.88 77 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__neg__pos_0) # label(axiom). [assumption].
% 1.57/1.88 78 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__pos__neg_0) # label(axiom). [assumption].
% 1.57/1.88 79 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__pos__neg2_0) # label(axiom). [assumption].
% 1.57/1.88 80 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) # label(cls_mult__less__imp__less__right_0) # label(axiom). [assumption].
% 1.57/1.88 81 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) # label(cls_mult__less__imp__less__left_0) # label(axiom). [assumption].
% 1.57/1.88 82 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__mono_0) # label(axiom). [assumption].
% 1.57/1.88 83 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__mono_H_0) # label(axiom). [assumption].
% 1.57/1.88 84 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) # label(cls_mult__right__le__imp__le_0) # label(axiom). [assumption].
% 1.57/1.88 85 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) # label(cls_mult__left__le__imp__le_0) # label(axiom). [assumption].
% 1.57/1.88 86 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__strict__right__mono_0) # label(axiom). [assumption].
% 1.57/1.88 87 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_mult__strict__left__mono_0) # label(axiom). [assumption].
% 1.57/1.88 88 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__le__less__imp__less_0) # label(axiom). [assumption].
% 1.57/1.88 89 -class_Ring__and__Field_Oordered__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_mult__less__le__imp__less_0) # label(axiom). [assumption].
% 1.57/1.88 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat). [resolve(73,a,74,a)].
% 1.57/1.88 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A),tc_nat). [resolve(73,a,75,a)].
% 1.57/1.88 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(73,a,76,a)].
% 1.57/1.88 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(73,a,77,a)].
% 1.57/1.88 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(73,a,78,a)].
% 1.57/1.88 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_nat). [resolve(73,a,80,a)].
% 1.57/1.88 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat). [resolve(73,a,81,a)].
% 1.57/1.88 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(73,a,82,a)].
% 1.57/1.88 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(73,a,83,a)].
% 1.57/1.88 Derived: c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_nat). [resolve(73,a,84,a)].
% 1.57/1.88 Derived: c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat). [resolve(73,a,85,a)].
% 1.57/1.88 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(73,a,86,a)].
% 1.57/1.88 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(73,a,87,a)].
% 1.57/1.88 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(73,a,88,a)].
% 1.57/1.88 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(73,a,89,a)].
% 1.57/1.88 90 class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 1.57/1.88 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),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint). [resolve(90,a,74,a)].
% 1.57/1.88 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),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),tc_Int_Oint). [resolve(90,a,75,a)].
% 1.57/1.88 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),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(90,a,76,a)].
% 1.57/1.88 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),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),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(90,a,77,a)].
% 1.57/1.88 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),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(90,a,78,a)].
% 1.57/1.88 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(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C),tc_Int_Oint). [resolve(90,a,80,a)].
% 1.57/1.88 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(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint). [resolve(90,a,81,a)].
% 1.65/1.97 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D),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(90,a,82,a)].
% 1.65/1.97 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D),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(90,a,83,a)].
% 1.65/1.97 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(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C),tc_Int_Oint). [resolve(90,a,84,a)].
% 1.65/1.97 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(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint). [resolve(90,a,85,a)].
% 1.65/1.97 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(90,a,86,a)].
% 1.65/1.97 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),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,C,tc_Int_Oint). [resolve(90,a,87,a)].
% 1.71/1.97 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D),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(90,a,88,a)].
% 1.71/1.97 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D),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(90,a,89,a)].
% 1.71/1.97 91 class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) # label(axiom). [assumption].
% 1.71/1.97 92 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__neg__neg_0) # label(axiom). [assumption].
% 1.71/1.97 93 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__sum__squares__lt__zero_0) # label(axiom). [assumption].
% 1.71/1.97 94 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_2) # label(axiom). [assumption].
% 1.71/1.97 95 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_0) # label(axiom). [assumption].
% 1.71/1.97 96 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_1) # label(axiom). [assumption].
% 1.71/1.97 97 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_2) # label(axiom). [assumption].
% 1.71/1.97 98 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_3) # label(axiom). [assumption].
% 1.71/1.97 99 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)),A) # label(cls_sum__squares__ge__zero_0) # label(axiom). [assumption].
% 1.71/1.97 100 -class_Ring__and__Field_Oordered__ring__strict(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_0) # label(axiom). [assumption].
% 1.71/1.97 101 -class_Ring__and__Field_Oordered__ring__strict(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_1) # label(axiom). [assumption].
% 1.71/1.97 102 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B),A) # label(cls_zero__le__square_0) # label(axiom). [assumption].
% 1.71/1.97 103 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__mult__iff_4) # label(axiom). [assumption].
% 1.71/1.97 104 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_zero__le__mult__iff_5) # label(axiom). [assumption].
% 1.71/1.97 105 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_zero__le__mult__iff_0) # label(axiom). [assumption].
% 1.71/1.97 106 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A) # label(cls_zero__le__mult__iff_1) # label(axiom). [assumption].
% 1.71/1.97 107 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_zero__le__mult__iff_2) # label(axiom). [assumption].
% 1.71/1.97 108 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A) # label(cls_zero__le__mult__iff_3) # label(axiom). [assumption].
% 1.71/1.97 109 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))),A) # label(cls_sum__squares__gt__zero__iff_0) # label(axiom). [assumption].
% 1.71/1.97 110 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_lessequals(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__le__cancel__left__pos_1) # label(axiom). [assumption].
% 1.71/1.97 111 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_mult__le__cancel__left__pos_0) # label(axiom). [assumption].
% 1.71/1.97 112 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_lessequals(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__cancel__left__neg_1) # label(axiom). [assumption].
% 1.71/1.97 113 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__cancel__left__neg_0) # label(axiom). [assumption].
% 1.71/1.97 114 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_1) # label(axiom). [assumption].
% 1.71/1.97 115 -class_Ring__and__Field_Oordered__ring__strict(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__squares__le__zero__iff_0) # label(axiom). [assumption].
% 1.71/1.97 116 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) # label(cls_mult__less__cancel__left__disj_0) # label(axiom). [assumption].
% 1.71/1.97 117 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A) # label(cls_mult__less__cancel__right__disj_0) # label(axiom). [assumption].
% 1.71/1.97 118 -class_Ring__and__Field_Oordered__ring__strict(A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__square__less__zero_0) # label(axiom). [assumption].
% 1.71/1.97 119 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__le__0__iff_4) # label(axiom). [assumption].
% 1.71/1.97 120 -class_Ring__and__Field_Oordered__ring__strict(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__le__0__iff_5) # label(axiom). [assumption].
% 1.71/1.97 121 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_2) # label(axiom). [assumption].
% 1.71/1.97 122 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C)),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__gt__zero__iff_1) # label(axiom). [assumption].
% 1.71/1.97 123 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(D,B,A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__right__disj_5) # label(axiom). [assumption].
% 1.71/1.97 124 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__less__cancel__right__disj_4) # label(axiom). [assumption].
% 1.71/1.97 125 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(D,B,A) # label(cls_mult__strict__right__mono__neg_0) # label(axiom). [assumption].
% 1.71/1.97 126 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__disj_5) # label(axiom). [assumption].
% 1.71/1.97 127 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__less__cancel__left__disj_4) # label(axiom). [assumption].
% 1.71/1.97 128 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(D,C,A) # label(cls_mult__strict__left__mono__neg_0) # label(axiom). [assumption].
% 1.71/1.97 129 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__less__cancel__left__pos_1) # label(axiom). [assumption].
% 1.71/1.97 130 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_mult__less__cancel__left__pos_0) # label(axiom). [assumption].
% 1.71/1.97 131 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(D,C,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__neg_1) # label(axiom). [assumption].
% 1.71/1.97 132 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A) | -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__less__cancel__left__neg_0) # label(axiom). [assumption].
% 1.71/1.97 133 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) # label(cls_mult__less__cancel__right__disj_3) # label(axiom). [assumption].
% 1.71/1.97 134 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A) # label(cls_mult__less__cancel__left__disj_3) # label(axiom). [assumption].
% 1.71/1.97 135 -class_Ring__and__Field_Oordered__ring__strict(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))) = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__squares__eq__zero__iff_2) # label(axiom). [assumption].
% 1.71/1.97 136 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A) # label(cls_mult__less__cancel__left__disj_1) # label(axiom). [assumption].
% 1.71/1.97 137 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) # label(cls_mult__less__cancel__left__disj_2) # label(axiom). [assumption].
% 1.71/1.97 138 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) # label(cls_mult__less__cancel__right__disj_1) # label(axiom). [assumption].
% 1.71/1.97 139 -class_Ring__and__Field_Oordered__ring__strict(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_HOL_Oord__class_Oless(C,D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A) # label(cls_mult__less__cancel__right__disj_2) # label(axiom). [assumption].
% 1.71/1.97 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),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(91,a,92,a)].
% 1.71/1.97 Derived: -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,93,a)].
% 1.71/1.97 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,94,a)].
% 1.71/1.97 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,95,a)].
% 1.71/1.97 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(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,96,a)].
% 1.71/1.97 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(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,97,a)].
% 1.71/1.97 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,98,a)].
% 1.71/1.97 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)),tc_Int_Oint). [resolve(91,a,99,a)].
% 1.71/1.97 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(91,a,100,a)].
% 1.71/1.97 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(91,a,101,a)].
% 1.71/1.97 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A),tc_Int_Oint). [resolve(91,a,102,a)].
% 1.71/1.97 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),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(91,a,103,a)].
% 1.71/1.97 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),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(91,a,104,a)].
% 1.71/1.97 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint). [resolve(91,a,105,a)].
% 1.71/1.97 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),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),tc_Int_Oint). [resolve(91,a,106,a)].
% 1.71/1.97 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),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint). [resolve(91,a,107,a)].
% 1.71/1.97 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),tc_Int_Oint). [resolve(91,a,108,a)].
% 1.71/1.97 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),tc_Int_Oint). [resolve(91,a,109,a)].
% 1.71/1.97 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),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(91,a,110,a)].
% 1.71/1.97 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),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(91,a,112,a)].
% 1.71/1.97 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,113,a)].
% 1.71/1.97 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,114,a)].
% 1.71/1.97 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,115,a)].
% 1.71/1.97 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(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint). [resolve(91,a,116,a)].
% 1.71/1.97 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(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),tc_Int_Oint). [resolve(91,a,117,a)].
% 1.71/1.97 Derived: -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,118,a)].
% 1.71/1.97 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),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(91,a,119,a)].
% 1.71/1.97 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),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(91,a,120,a)].
% 1.71/1.97 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)),tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(91,a,121,a)].
% 1.71/1.97 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B)),tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(91,a,122,a)].
% 1.71/1.97 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),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(91,a,123,a)].
% 1.71/1.97 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),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(91,a,126,a)].
% 1.71/1.97 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint). [resolve(91,a,130,a)].
% 1.71/2.05 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(91,a,132,a)].
% 1.71/2.05 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(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint). [resolve(91,a,133,a)].
% 1.71/2.05 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(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),tc_Int_Oint). [resolve(91,a,134,a)].
% 1.71/2.05 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(91,a,135,a)].
% 1.71/2.05 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(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),tc_Int_Oint). [resolve(91,a,136,a)].
% 1.71/2.05 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(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint). [resolve(91,a,137,a)].
% 1.71/2.05 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(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint). [resolve(91,a,138,a)].
% 1.71/2.05 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(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),tc_Int_Oint). [resolve(91,a,139,a)].
% 1.71/2.05 140 class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) # label(axiom). [assumption].
% 1.71/2.05 141 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__less__zero__iff__single__less__zero_1) # label(axiom). [assumption].
% 1.71/2.05 142 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__less__zero__iff__single__less__zero_0) # label(axiom). [assumption].
% 1.71/2.05 143 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_double__eq__0__iff_0) # label(axiom). [assumption].
% 1.71/2.05 144 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ouminus__class_Ouminus(C,A),A) # label(cls_le__eq__neg_0) # label(axiom). [assumption].
% 1.71/2.05 145 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ouminus__class_Ouminus(C,A),A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) # label(cls_le__eq__neg_1) # label(axiom). [assumption].
% 1.71/2.05 146 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_double__eq__0__iff_1) # label(axiom). [assumption].
% 1.71/2.05 147 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A) # label(cls_zero__less__double__add__iff__zero__less__single__add_0) # label(axiom). [assumption].
% 1.71/2.05 148 -class_OrderedGroup_Olordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__less__double__add__iff__zero__less__single__add_1) # label(axiom). [assumption].
% 1.71/2.05 149 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A) # label(cls_zero__le__double__add__iff__zero__le__single__add_0) # label(axiom). [assumption].
% 1.71/2.05 150 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__double__add__iff__zero__le__single__add_1) # label(axiom). [assumption].
% 1.71/2.05 151 -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].
% 1.71/2.05 152 -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].
% 1.71/2.05 153 -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].
% 1.71/2.05 154 -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].
% 1.71/2.05 155 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__le__zero__iff__single__add__le__zero_0) # label(axiom). [assumption].
% 1.71/2.05 156 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_double__add__le__zero__iff__single__add__le__zero_1) # label(axiom). [assumption].
% 1.71/2.05 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A),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(140,a,141,a)].
% 1.71/2.05 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(140,a,142,a)].
% 1.71/2.05 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(140,a,143,a)].
% 1.71/2.05 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),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(140,a,144,a)].
% 1.71/2.05 Derived: c_lessequals(A,c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(140,a,145,a)].
% 1.71/2.05 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(140,a,146,a)].
% 1.82/2.12 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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A),tc_Int_Oint). [resolve(140,a,147,a)].
% 1.82/2.12 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(140,a,148,a)].
% 1.82/2.12 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),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A),tc_Int_Oint). [resolve(140,a,149,a)].
% 1.82/2.12 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(140,a,150,a)].
% 1.82/2.12 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(140,a,151,a)].
% 1.82/2.12 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(140,a,152,a)].
% 1.82/2.12 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(140,a,153,a)].
% 1.82/2.12 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(140,a,154,a)].
% 1.82/2.12 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(140,a,155,a)].
% 1.82/2.12 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A),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(140,a,156,a)].
% 1.82/2.12 157 class_Ring__and__Field_Oordered__idom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__idom) # label(axiom). [assumption].
% 1.82/2.12 158 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_even__less__0__iff_0) # label(axiom). [assumption].
% 1.82/2.12 159 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_even__less__0__iff_1) # label(axiom). [assumption].
% 1.82/2.12 160 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_abs__less__iff_1) # label(axiom). [assumption].
% 1.82/2.12 161 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oabs__class_Oabs(B,A)),c_HOL_Oabs__class_Oabs(C,A)) # label(cls_abs__mult_0) # label(axiom). [assumption].
% 1.82/2.12 162 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(B,A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_abs__less__iff_2) # label(axiom). [assumption].
% 1.82/2.12 163 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(B,A),A) = c_HOL_Ouminus__class_Ouminus(c_Int_Onumber__class_Onumber__of(B,A),A) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__number__of_0) # label(axiom). [assumption].
% 1.82/2.12 164 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(B,tc_nat)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq__number__of_0) # label(axiom). [assumption].
% 1.82/2.12 165 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oabs__class_Oabs(B,A)),c_HOL_Oabs__class_Oabs(C,A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(C,A),E,A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(B,A),D,A) # label(cls_abs__mult__less_0) # label(axiom). [assumption].
% 1.82/2.12 166 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(A),A) = c_HOL_Oone__class_Oone(A) # label(cls_abs__one_0) # label(axiom). [assumption].
% 1.82/2.12 167 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq_3) # label(axiom). [assumption].
% 1.82/2.12 168 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(B,A),A) = c_Nat_Osemiring__1__class_Oof__nat(B,A) # label(cls_abs__of__nat_0) # label(axiom). [assumption].
% 1.82/2.12 169 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),C,A) | -c_lessequals(B,c_HOL_Oone__class_Oone(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__left__le__one__le_0) # label(axiom). [assumption].
% 1.82/2.12 170 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),B,A) | -c_lessequals(C,c_HOL_Oone__class_Oone(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__right__le__one__le_0) # label(axiom). [assumption].
% 1.82/2.12 171 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_abs__less__iff_0) # label(axiom). [assumption].
% 1.82/2.12 172 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Oabs__class_Oabs(B,A)),C),A) # label(cls_zero__le__power__abs_0) # label(axiom). [assumption].
% 1.82/2.12 173 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__power__iff_1) # label(axiom). [assumption].
% 1.82/2.12 174 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(B,A),A) = c_Int_Onumber__class_Onumber__of(B,A) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__number__of_1) # label(axiom). [assumption].
% 1.82/2.12 175 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Ozero__class_Ozero(tc_nat)),A) # label(cls_zero__less__power__eq_3) # label(axiom). [assumption].
% 1.82/2.12 176 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_zero__less__power__eq_2) # label(axiom). [assumption].
% 1.82/2.12 177 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Oabs__class_Oabs(B,A)),C) # label(cls_power__abs_0) # label(axiom). [assumption].
% 1.82/2.12 178 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oabs__class_Oabs(B,A)),c_HOL_Oabs__class_Oabs(B,A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B) # label(cls_abs__mult__self_0) # label(axiom). [assumption].
% 1.82/2.12 179 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ouminus__class_Ouminus(B,A)),C),A) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) # label(cls_abs__power__minus_0) # label(axiom). [assumption].
% 1.82/2.12 180 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oabs__class_Oabs(B,A)),C) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_abs__mult__pos_0) # label(axiom). [assumption].
% 1.82/2.12 181 -class_Ring__and__Field_Oordered__idom(A) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq_0) # label(axiom). [assumption].
% 1.82/2.12 182 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq__number__of_3) # label(axiom). [assumption].
% 1.82/2.12 183 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C))),A) # label(cls_odd__0__le__power__imp__0__le_0) # label(axiom). [assumption].
% 1.82/2.12 184 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_Int_OPls,tc_Int_Oint) # label(cls_less__special_I3_J_1) # label(axiom). [assumption].
% 1.82/2.12 185 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oord__class_Oless(B,c_Int_OPls,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_less__special_I3_J_0) # label(axiom). [assumption].
% 1.82/2.12 186 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,A),A) | -c_HOL_Oord__class_Oless(c_Int_OPls,B,tc_Int_Oint) # label(cls_less__special_I1_J_1) # label(axiom). [assumption].
% 1.82/2.12 187 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oord__class_Oless(c_Int_OPls,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_less__special_I1_J_0) # label(axiom). [assumption].
% 1.82/2.12 188 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat)),A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_zero__less__power__eq__number__of_2) # label(axiom). [assumption].
% 1.82/2.12 189 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(B,tc_nat)),A) # label(cls_zero__less__power__eq__number__of_3) # label(axiom). [assumption].
% 1.82/2.12 190 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__power2__le__zero__iff_1) # label(axiom). [assumption].
% 1.82/2.12 191 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__power2__le__zero__iff_0) # label(axiom). [assumption].
% 1.82/2.12 192 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C)),A) # label(cls_zero__le__even__power_H_0) # label(axiom). [assumption].
% 1.82/2.12 193 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(A),A) # label(cls_sum__power2__le__zero__iff_2) # label(axiom). [assumption].
% 1.82/2.12 194 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_even__power__le__0__imp__0_0) # label(axiom). [assumption].
% 1.82/2.12 195 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),A) # label(cls_sum__power2__ge__zero_0) # label(axiom). [assumption].
% 1.82/2.12 196 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oord__class_Oless(B,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) # label(cls_less__number__of_0) # label(axiom). [assumption].
% 1.82/2.12 197 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) | -c_HOL_Oord__class_Oless(B,C,tc_Int_Oint) # label(cls_less__number__of_1) # label(axiom). [assumption].
% 1.82/2.12 198 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__less__zero__eq_1) # label(axiom). [assumption].
% 1.82/2.12 199 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(B,c_Int_OBit1(c_Int_OPls),tc_Int_Oint) # label(cls_less__special_I4_J_1) # label(axiom). [assumption].
% 1.82/2.12 200 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oord__class_Oless(B,c_Int_OBit1(c_Int_OPls),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oone__class_Oone(A),A) # label(cls_less__special_I4_J_0) # label(axiom). [assumption].
% 1.82/2.12 201 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(B,A),A) | -c_HOL_Oord__class_Oless(c_Int_OBit1(c_Int_OPls),B,tc_Int_Oint) # label(cls_less__special_I2_J_1) # label(axiom). [assumption].
% 1.82/2.12 202 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | c_HOL_Oord__class_Oless(c_Int_OBit1(c_Int_OPls),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_less__special_I2_J_0) # label(axiom). [assumption].
% 1.82/2.12 203 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C))),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_odd__power__less__zero_0) # label(axiom). [assumption].
% 1.82/2.12 204 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ouminus__class_Ouminus(B,A),A) # label(cls_less__minus__self__iff_0) # label(axiom). [assumption].
% 1.82/2.12 205 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ouminus__class_Ouminus(B,A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_less__minus__self__iff_1) # label(axiom). [assumption].
% 1.82/2.12 206 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__power2__eq__zero__iff_2) # label(axiom). [assumption].
% 1.82/2.12 207 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__power2__eq__zero__iff_1) # label(axiom). [assumption].
% 1.82/2.12 208 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__power2__eq__zero__iff_0) # label(axiom). [assumption].
% 1.82/2.12 209 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A) # label(cls_zero__le__power2_0) # label(axiom). [assumption].
% 1.82/2.12 210 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__less__zero__eq__number__of_1) # label(axiom). [assumption].
% 1.82/2.12 211 -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),A) # label(cls_sum__power2__gt__zero__iff_0) # label(axiom). [assumption].
% 1.82/2.12 212 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__power2__gt__zero__iff_2) # label(axiom). [assumption].
% 1.82/2.12 213 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__power2__gt__zero__iff_1) # label(axiom). [assumption].
% 1.82/2.12 214 -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(A),A) # label(cls_not__sum__power2__lt__zero_0) # label(axiom). [assumption].
% 1.82/2.12 215 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = c_HOL_Ozero__class_Ozero(A) # label(cls_zero__eq__power2_1) # label(axiom). [assumption].
% 1.82/2.12 216 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_zero__eq__power2_0) # label(axiom). [assumption].
% 1.82/2.12 217 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Oabs__class_Oabs(B,A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) # label(cls_power2__abs_0) # label(axiom). [assumption].
% 1.82/2.12 218 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) # label(cls_abs__power2_0) # label(axiom). [assumption].
% 1.82/2.12 219 -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power2__less__0_0) # label(axiom). [assumption].
% 1.82/2.12 220 -class_Ring__and__Field_Oordered__idom(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A) # label(cls_zero__less__power2_0) # label(axiom). [assumption].
% 1.82/2.12 221 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_zero__less__power2_1) # label(axiom). [assumption].
% 1.82/2.12 222 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE__ordered__idom_0) # label(axiom). [assumption].
% 1.82/2.12 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_Oabs__class_Oabs(A,tc_Int_Oint),B,tc_Int_Oint). [resolve(157,a,160,a)].
% 1.82/2.12 Derived: c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oabs__class_Oabs(A,tc_Int_Oint)),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint)). [resolve(157,a,161,a)].
% 1.82/2.12 Derived: c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(157,a,162,a)].
% 1.86/2.12 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(157,a,163,a)].
% 1.86/2.12 Derived: c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(A,tc_nat)),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(157,a,164,a)].
% 1.86/2.12 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oabs__class_Oabs(A,tc_Int_Oint)),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(B,tc_Int_Oint),D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),C,tc_Int_Oint). [resolve(157,a,165,a)].
% 1.86/2.12 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(157,a,166,a)].
% 1.86/2.12 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(157,a,167,a)].
% 1.86/2.12 Derived: c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint),tc_Int_Oint) = c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint). [resolve(157,a,168,a)].
% 1.86/2.12 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),B,tc_Int_Oint) | -c_lessequals(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(157,a,169,a)].
% 1.86/2.12 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),A,tc_Int_Oint) | -c_lessequals(B,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(157,a,170,a)].
% 1.86/2.12 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),B,tc_Int_Oint). [resolve(157,a,171,a)].
% 1.86/2.12 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Oabs__class_Oabs(A,tc_Int_Oint)),B),tc_Int_Oint). [resolve(157,a,172,a)].
% 1.86/2.12 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(157,a,173,a)].
% 1.86/2.12 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(157,a,174,a)].
% 1.86/2.12 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_nat)),tc_Int_Oint). [resolve(157,a,175,a)].
% 1.86/2.12 Derived: A = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),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_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(157,a,176,a)].
% 1.86/2.12 Derived: c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Oabs__class_Oabs(A,tc_Int_Oint)),B). [resolve(157,a,177,a)].
% 1.86/2.12 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oabs__class_Oabs(A,tc_Int_Oint)),c_HOL_Oabs__class_Oabs(A,tc_Int_Oint)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A). [resolve(157,a,178,a)].
% 1.86/2.12 Derived: c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint)),B),tc_Int_Oint) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint). [resolve(157,a,179,a)].
% 1.86/2.12 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oabs__class_Oabs(A,tc_Int_Oint)),B) = c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(157,a,180,a)].
% 1.86/2.12 Derived: -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(157,a,181,a)].
% 1.86/2.12 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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Suc(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B))),tc_Int_Oint). [resolve(157,a,183,a)].
% 1.86/2.12 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_Int_OPls,tc_Int_Oint). [resolve(157,a,184,a)].
% 1.86/2.12 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oord__class_Oless(A,c_Int_OPls,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(157,a,185,a)].
% 1.86/2.12 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Int_OPls,A,tc_Int_Oint). [resolve(157,a,186,a)].
% 1.86/2.12 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oord__class_Oless(c_Int_OPls,A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint). [resolve(157,a,187,a)].
% 1.86/2.12 Derived: c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(A,tc_nat)),tc_Int_Oint). [resolve(157,a,189,a)].
% 1.86/2.12 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(157,a,190,a)].
% 1.86/2.12 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(157,a,191,a)].
% 1.86/2.12 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)),tc_Int_Oint). [resolve(157,a,192,a)].
% 1.86/2.12 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(157,a,193,a)].
% 1.86/2.12 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(157,a,194,a)].
% 1.86/2.12 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),tc_Int_Oint). [resolve(157,a,195,a)].
% 1.86/2.12 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oord__class_Oless(A,B,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). [resolve(157,a,196,a)].
% 1.86/2.12 Derived: -class_Int_Onumber__ring(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_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(157,a,197,a)].
% 1.86/2.12 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(157,a,198,a)].
% 1.86/2.12 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_Int_OBit1(c_Int_OPls),tc_Int_Oint). [resolve(157,a,199,a)].
% 1.86/2.12 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oord__class_Oless(A,c_Int_OBit1(c_Int_OPls),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(157,a,200,a)].
% 1.86/2.12 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_Int_OBit1(c_Int_OPls),A,tc_Int_Oint). [resolve(157,a,201,a)].
% 1.86/2.12 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Oord__class_Oless(c_Int_OBit1(c_Int_OPls),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint). [resolve(157,a,202,a)].
% 1.86/2.12 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Suc(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),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(157,a,203,a)].
% 1.86/2.12 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint). [resolve(157,a,204,a)].
% 1.86/2.12 Derived: c_HOL_Oord__class_Oless(A,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(157,a,205,a)].
% 1.86/2.12 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(157,a,206,a)].
% 1.86/2.12 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(157,a,207,a)].
% 1.86/2.12 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(157,a,208,a)].
% 1.86/2.12 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_Int_Oint). [resolve(157,a,209,a)].
% 1.86/2.12 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),tc_Int_Oint). [resolve(157,a,211,a)].
% 1.86/2.12 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(157,a,212,a)].
% 1.86/2.12 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(157,a,213,a)].
% 1.86/2.12 Derived: -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(157,a,214,a)].
% 1.86/2.12 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(157,a,215,a)].
% 1.86/2.12 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(157,a,216,a)].
% 1.86/2.12 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Oabs__class_Oabs(A,tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(157,a,217,a)].
% 1.86/2.12 Derived: c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(157,a,218,a)].
% 1.86/2.12 Derived: -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(157,a,219,a)].
% 1.95/2.26 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_Int_Oint). [resolve(157,a,220,a)].
% 1.95/2.26 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(157,a,221,a)].
% 1.95/2.26 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(B,A,tc_Int_Oint) | B = A. [resolve(157,a,222,a)].
% 1.95/2.26 223 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].
% 1.95/2.26 224 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_0) # label(axiom). [assumption].
% 1.95/2.26 225 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_1) # label(axiom). [assumption].
% 1.95/2.26 226 -class_Ring__and__Field_Oring__no__zero__divisors(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__eq__0__iff_2) # label(axiom). [assumption].
% 1.95/2.26 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B) != 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(223,a,224,a)].
% 1.95/2.26 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(223,a,225,a)].
% 1.95/2.26 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(223,a,226,a)].
% 1.95/2.26 227 class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) # label(axiom). [assumption].
% 1.95/2.26 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(227,a,224,a)].
% 1.95/2.26 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(227,a,225,a)].
% 1.95/2.26 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(227,a,226,a)].
% 1.95/2.26 228 class_Ring__and__Field_Ono__zero__divisors(tc_nat) # label(clsarity_nat__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 1.95/2.26 229 -class_Ring__and__Field_Ono__zero__divisors(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_no__zero__divisors_0) # label(axiom). [assumption].
% 1.95/2.26 230 -class_Ring__and__Field_Ono__zero__divisors(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_no__zero__divirors__neq0_0) # label(axiom). [assumption].
% 1.95/2.26 231 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__eq__0__iff_2) # label(axiom). [assumption].
% 1.95/2.26 232 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_1) # label(axiom). [assumption].
% 1.95/2.26 233 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_0) # label(axiom). [assumption].
% 1.95/2.26 234 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat)) = 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].
% 1.95/2.26 235 -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) | hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(B,tc_nat)) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff__number__of_1) # label(axiom). [assumption].
% 1.95/2.26 236 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)) != 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].
% 1.95/2.26 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(228,a,229,a)].
% 1.95/2.26 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(228,a,231,b)].
% 1.95/2.26 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(228,a,232,b)].
% 1.95/2.26 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(228,a,233,b)].
% 1.95/2.26 Derived: -class_Ring__and__Field_Ozero__neq__one(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) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),c_Int_Onumber__class_Onumber__of(A,tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(228,a,235,b)].
% 1.95/2.26 237 class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 1.95/2.26 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(237,a,231,b)].
% 1.95/2.26 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(237,a,232,b)].
% 2.02/2.33 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(237,a,233,b)].
% 2.02/2.33 Derived: -class_Ring__and__Field_Ozero__neq__one(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) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(A,tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(237,a,235,b)].
% 2.02/2.33 238 class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 2.02/2.33 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(238,a,231,b)].
% 2.02/2.33 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(238,a,232,b)].
% 2.02/2.33 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(238,a,233,b)].
% 2.02/2.33 Derived: -class_Ring__and__Field_Ozero__neq__one(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) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),c_Int_Onumber__class_Onumber__of(A,tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(238,a,235,b)].
% 2.02/2.33 239 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 2.02/2.33 240 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_1) # label(axiom). [assumption].
% 2.02/2.33 241 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_0) # label(axiom). [assumption].
% 2.02/2.33 242 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__neg__nonpos_0) # label(axiom). [assumption].
% 2.02/2.33 243 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__nonpos__neg_0) # label(axiom). [assumption].
% 2.02/2.33 244 -class_OrderedGroup_Opordered__comm__monoid__add(A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_2) # label(axiom). [assumption].
% 2.02/2.33 245 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 2.02/2.33 246 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__nonneg__pos_0) # label(axiom). [assumption].
% 2.02/2.33 247 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__pos__nonneg_0) # label(axiom). [assumption].
% 2.02/2.33 248 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__nonneg__nonneg_0) # label(axiom). [assumption].
% 2.02/2.33 249 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 2.02/2.33 250 -class_OrderedGroup_Opordered__comm__monoid__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_add__nonpos__nonpos_0) # label(axiom). [assumption].
% 2.02/2.33 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(239,a,240,a)].
% 2.02/2.33 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(239,a,241,a)].
% 2.02/2.33 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(239,a,242,a)].
% 2.02/2.33 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(239,a,243,a)].
% 2.02/2.33 Derived: -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(239,a,244,a)].
% 2.02/2.33 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(239,a,245,a)].
% 2.02/2.33 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(239,a,246,a)].
% 2.02/2.33 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(239,a,247,a)].
% 2.02/2.33 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(239,a,248,a)].
% 2.02/2.33 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(239,a,249,a)].
% 2.02/2.33 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(239,a,250,a)].
% 2.02/2.33 251 class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 2.02/2.33 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != 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(251,a,240,a)].
% 2.02/2.33 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != 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(251,a,241,a)].
% 2.02/2.33 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),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(251,a,242,a)].
% 2.02/2.33 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),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(251,a,243,a)].
% 2.02/2.33 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),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(251,a,245,a)].
% 2.02/2.33 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),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(251,a,246,a)].
% 2.02/2.33 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),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_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(251,a,247,a)].
% 2.02/2.33 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),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(251,a,248,a)].
% 2.16/2.45 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),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(251,a,249,a)].
% 2.16/2.45 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),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(251,a,250,a)].
% 2.16/2.45 252 class_OrderedGroup_Ogroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 2.16/2.45 253 -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].
% 2.16/2.45 254 -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].
% 2.16/2.45 255 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ouminus__class_Ouminus(B,A)),C)) = C # label(cls_add__minus__cancel_0) # label(axiom). [assumption].
% 2.16/2.45 256 -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].
% 2.16/2.45 257 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ouminus__class_Ouminus(B,A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__neg__iff__add__eq__0_0) # label(axiom). [assumption].
% 2.16/2.45 258 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ouminus__class_Ouminus(B,A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus_0) # label(axiom). [assumption].
% 2.16/2.45 259 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ouminus__class_Ouminus(B,A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_left__minus_0) # label(axiom). [assumption].
% 2.16/2.45 260 -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].
% 2.16/2.45 261 -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].
% 2.16/2.45 262 -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].
% 2.16/2.45 263 -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].
% 2.16/2.45 264 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | c_HOL_Ouminus__class_Ouminus(B,A) = C # label(cls_minus__unique_0) # label(axiom). [assumption].
% 2.16/2.45 265 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ouminus__class_Ouminus(C,A) # label(cls_eq__neg__iff__add__eq__0_1) # label(axiom). [assumption].
% 2.16/2.45 266 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ouminus__class_Ouminus(B,A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)) = C # label(cls_minus__add__cancel_0) # label(axiom). [assumption].
% 2.16/2.45 267 -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].
% 2.16/2.45 268 -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].
% 2.16/2.45 269 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ouminus__class_Ouminus(C,A)),c_HOL_Ouminus__class_Ouminus(B,A)) # label(cls_minus__add_0) # label(axiom). [assumption].
% 2.16/2.45 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(252,a,253,a)].
% 2.16/2.45 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint) != c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint) | A = B. [resolve(252,a,254,a)].
% 2.16/2.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint)),B)) = B. [resolve(252,a,255,a)].
% 2.16/2.45 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(252,a,256,a)].
% 2.16/2.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint)),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(252,a,257,a)].
% 2.16/2.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(252,a,258,a)].
% 2.16/2.45 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint) = A. [resolve(252,a,260,a)].
% 2.16/2.45 Derived: A = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint). [resolve(252,a,261,a)].
% 2.16/2.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint) = B. [resolve(252,a,264,a)].
% 2.16/2.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint). [resolve(252,a,265,a)].
% 2.16/2.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)) = B. [resolve(252,a,266,a)].
% 2.16/2.45 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(252,a,267,a)].
% 2.16/2.45 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(252,a,268,a)].
% 2.16/2.45 Derived: c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint)),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint)). [resolve(252,a,269,a)].
% 2.16/2.45 270 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 2.16/2.45 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(270,a,253,a)].
% 2.16/2.45 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex) | A = B. [resolve(270,a,254,a)].
% 2.16/2.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),B)) = B. [resolve(270,a,255,a)].
% 2.16/2.45 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(270,a,256,a)].
% 2.16/2.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(270,a,257,a)].
% 2.16/2.45 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(270,a,258,a)].
% 2.16/2.45 Derived: c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(270,a,260,a)].
% 2.16/2.45 Derived: A = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(270,a,261,a)].
% 2.16/2.48 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex) = B. [resolve(270,a,264,a)].
% 2.16/2.48 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex). [resolve(270,a,265,a)].
% 2.16/2.48 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)) = B. [resolve(270,a,266,a)].
% 2.16/2.48 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(270,a,267,a)].
% 2.16/2.48 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(270,a,268,a)].
% 2.16/2.48 Derived: c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex)),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)). [resolve(270,a,269,a)].
% 2.16/2.48 271 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 2.16/2.48 272 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) # label(cls_class__semiring_Osemiring__rules_I13_J_0) # label(axiom). [assumption].
% 2.16/2.48 273 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) # label(cls_class__semiring_Osemiring__rules_I14_J_0) # label(axiom). [assumption].
% 2.16/2.48 274 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),E)) # label(cls_class__semiring_Osemiring__rules_I15_J_0) # label(axiom). [assumption].
% 2.16/2.48 275 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(A) # label(cls_class__semiring_Opwr__0_0) # label(axiom). [assumption].
% 2.16/2.48 276 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) # label(cls_class__semiring_Omul__pwr_0) # label(axiom). [assumption].
% 2.16/2.48 277 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_class__semiring_Omul__1_0) # label(axiom). [assumption].
% 2.16/2.48 278 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oone__class_Oone(A)) = B # label(cls_class__semiring_Osemiring__rules_I12_J_0) # label(axiom). [assumption].
% 2.16/2.48 279 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_class__semiring_Osemiring__rules_I11_J_0) # label(axiom). [assumption].
% 2.16/2.48 280 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_class__semiring_Opwr__Suc_0) # label(axiom). [assumption].
% 2.16/2.49 281 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_class__semiring_Osemiring__rules_I35_J_0) # label(axiom). [assumption].
% 2.16/2.49 282 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B) # label(cls_class__semiring_Omul__c_0) # label(axiom). [assumption].
% 2.16/2.49 283 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I16_J_0) # label(axiom). [assumption].
% 2.16/2.49 284 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I17_J_0) # label(axiom). [assumption].
% 2.16/2.49 285 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) # label(cls_class__semiring_Osemiring__rules_I18_J_0) # label(axiom). [assumption].
% 2.16/2.49 286 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I19_J_0) # label(axiom). [assumption].
% 2.16/2.49 287 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) # label(cls_class__semiring_Omul__a_0) # label(axiom). [assumption].
% 2.16/2.49 288 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I8_J_0) # label(axiom). [assumption].
% 2.16/2.49 289 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_class__semiring_Omul__d_0) # label(axiom). [assumption].
% 2.16/2.49 290 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I1_J_0) # label(axiom). [assumption].
% 2.16/2.49 291 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B) # label(cls_class__semiring_Osemiring__rules_I7_J_0) # label(axiom). [assumption].
% 2.16/2.49 292 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Oadd__a_0) # label(axiom). [assumption].
% 2.16/2.49 293 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Osemiring__rules_I25_J_0) # label(axiom). [assumption].
% 2.16/2.49 294 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I23_J_0) # label(axiom). [assumption].
% 2.16/2.49 295 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I22_J_0) # label(axiom). [assumption].
% 2.16/2.49 296 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I21_J_0) # label(axiom). [assumption].
% 2.16/2.49 297 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E)) # label(cls_class__semiring_Osemiring__rules_I20_J_0) # label(axiom). [assumption].
% 2.16/2.49 298 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_class__semiring_Ogb__semiring__axioms_H_0) # label(axiom). [assumption].
% 2.16/2.49 299 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Oadd__0_0) # label(axiom). [assumption].
% 2.16/2.49 300 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_class__semiring_Osemiring__rules_I6_J_0) # label(axiom). [assumption].
% 2.16/2.49 301 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Osemiring__rules_I5_J_0) # label(axiom). [assumption].
% 2.16/2.49 302 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Osemiring__rules_I24_J_0) # label(axiom). [assumption].
% 2.16/2.49 303 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Oadd__c_0) # label(axiom). [assumption].
% 2.16/2.49 304 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Oone__class_Oone(tc_nat)) = B # label(cls_class__semiring_Osemiring__rules_I33_J_0) # label(axiom). [assumption].
% 2.16/2.49 305 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) # label(cls_class__semiring_Opwr__mul_0) # label(axiom). [assumption].
% 2.16/2.49 306 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) # label(cls_class__semiring_Opwr__pwr_0) # label(axiom). [assumption].
% 2.16/2.49 307 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A))),B) # label(cls_class__semiring_Osemiring__rules_I4_J_0) # label(axiom). [assumption].
% 2.16/2.49 308 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I9_J_0) # label(axiom). [assumption].
% 2.16/2.49 309 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I10_J_0) # label(axiom). [assumption].
% 2.16/2.49 310 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Omul__0_0) # label(axiom). [assumption].
% 2.16/2.49 311 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A))),C) # label(cls_class__semiring_Osemiring__rules_I2_J_0) # label(axiom). [assumption].
% 2.16/2.49 312 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),c_HOL_Oone__class_Oone(A))),B) # label(cls_class__semiring_Osemiring__rules_I3_J_0) # label(axiom). [assumption].
% 2.16/2.49 313 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)) # label(cls_class__semiring_Osemiring__rules_I27_J_0) # label(axiom). [assumption].
% 2.16/2.49 314 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)) # label(cls_class__semiring_Osemiring__rules_I28_J_0) # label(axiom). [assumption].
% 2.16/2.49 315 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) # label(cls_class__semiring_Osemiring__rules_I37_J_0) # label(axiom). [assumption].
% 2.16/2.49 316 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_class__semiring_Osemiring__rules_I36_J_0) # label(axiom). [assumption].
% 2.16/2.49 317 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) # label(cls_class__semiring_Osemiring__rules_I29_J_0) # label(axiom). [assumption].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),D)). [resolve(271,a,272,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))). [resolve(271,a,273,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),D)). [resolve(271,a,274,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat). [resolve(271,a,275,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(271,a,276,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = A. [resolve(271,a,277,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(271,a,278,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)). [resolve(271,a,280,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(271,a,282,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),B). [resolve(271,a,283,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(271,a,284,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C). [resolve(271,a,285,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)). [resolve(271,a,286,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(271,a,288,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)). [resolve(271,a,289,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B). [resolve(271,a,290,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C). [resolve(271,a,292,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B). [resolve(271,a,294,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)). [resolve(271,a,295,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(271,a,296,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),D)). [resolve(271,a,297,a)].
% 2.16/2.49 Derived: c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(tc_nat),c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(271,a,298,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(271,a,299,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(271,a,300,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(271,a,302,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(271,a,304,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),C)). [resolve(271,a,305,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(271,a,306,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),A). [resolve(271,a,307,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(271,a,308,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(271,a,309,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))),B). [resolve(271,a,311,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))),A). [resolve(271,a,312,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)). [resolve(271,a,313,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),A) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)). [resolve(271,a,314,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B))). [resolve(271,a,315,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)). [resolve(271,a,316,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),A) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(271,a,317,a)].
% 2.16/2.49 318 class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D)). [resolve(318,a,272,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))). [resolve(318,a,273,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),D)). [resolve(318,a,274,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(318,a,275,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(318,a,276,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),A) = A. [resolve(318,a,277,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(318,a,278,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)). [resolve(318,a,280,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A). [resolve(318,a,282,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)),B). [resolve(318,a,283,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)). [resolve(318,a,284,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C). [resolve(318,a,285,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)). [resolve(318,a,286,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)). [resolve(318,a,288,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)). [resolve(318,a,289,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C)),B). [resolve(318,a,290,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),C). [resolve(318,a,292,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C)),B). [resolve(318,a,294,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C)). [resolve(318,a,295,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)). [resolve(318,a,296,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),D)). [resolve(318,a,297,a)].
% 2.16/2.49 Derived: c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(318,a,298,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A) = A. [resolve(318,a,299,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(318,a,300,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),A). [resolve(318,a,302,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(318,a,304,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C)). [resolve(318,a,305,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(318,a,306,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),c_HOL_Oone__class_Oone(tc_Int_Oint))),A). [resolve(318,a,307,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint))),B). [resolve(318,a,311,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),c_HOL_Oone__class_Oone(tc_Int_Oint))),A). [resolve(318,a,312,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Suc(B)). [resolve(318,a,313,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),A) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Suc(B)). [resolve(318,a,314,a)].
% 2.16/2.49 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Suc(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))). [resolve(318,a,315,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)). [resolve(318,a,316,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(318,a,317,a)].
% 2.16/2.50 319 class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 2.16/2.50 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)). [resolve(319,a,272,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D))). [resolve(319,a,273,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),D)). [resolve(319,a,274,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(319,a,275,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(319,a,276,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A) = A. [resolve(319,a,277,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(319,a,278,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)). [resolve(319,a,280,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A). [resolve(319,a,282,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),B). [resolve(319,a,283,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)). [resolve(319,a,284,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C). [resolve(319,a,285,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)). [resolve(319,a,286,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)). [resolve(319,a,288,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)). [resolve(319,a,289,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)),B). [resolve(319,a,290,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C). [resolve(319,a,292,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)),B). [resolve(319,a,294,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)). [resolve(319,a,295,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)). [resolve(319,a,296,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),D)). [resolve(319,a,297,a)].
% 2.16/2.50 Derived: c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(319,a,298,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = A. [resolve(319,a,299,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(319,a,300,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),A). [resolve(319,a,302,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(319,a,304,a)].
% 2.16/2.50 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B),C)). [resolve(319,a,305,a)].
% 2.26/2.54 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(319,a,306,a)].
% 2.26/2.54 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),A). [resolve(319,a,307,a)].
% 2.26/2.54 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),B). [resolve(319,a,311,a)].
% 2.26/2.54 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),A). [resolve(319,a,312,a)].
% 2.26/2.54 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Suc(B)). [resolve(319,a,313,a)].
% 2.26/2.54 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),A) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Suc(B)). [resolve(319,a,314,a)].
% 2.26/2.54 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Suc(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B))). [resolve(319,a,315,a)].
% 2.26/2.54 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)). [resolve(319,a,316,a)].
% 2.26/2.54 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),A) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(319,a,317,a)].
% 2.26/2.54 320 class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs) # label(axiom). [assumption].
% 2.26/2.54 321 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__le__zero__iff_0) # label(axiom). [assumption].
% 2.26/2.54 322 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = B | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__of__nonneg_0) # label(axiom). [assumption].
% 2.26/2.54 323 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_abs__le__D2_0) # label(axiom). [assumption].
% 2.26/2.54 324 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = c_HOL_Ouminus__class_Ouminus(B,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__of__neg_0) # label(axiom). [assumption].
% 2.26/2.54 325 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(B,A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__minus__le__zero_0) # label(axiom). [assumption].
% 2.26/2.54 326 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Oabs__class_Oabs(B,A),C,A) # label(cls_abs__le__D1_0) # label(axiom). [assumption].
% 2.26/2.54 327 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_abs__eq__0_1) # label(axiom). [assumption].
% 2.26/2.54 328 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oabs__class_Oabs(B,A)),c_HOL_Oabs__class_Oabs(C,A)),A) # label(cls_abs__triangle__ineq_0) # label(axiom). [assumption].
% 2.26/2.54 329 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = B | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__of__pos_0) # label(axiom). [assumption].
% 2.26/2.54 330 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(B,A),C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(B,C,A) # label(cls_abs__leI_0) # label(axiom). [assumption].
% 2.26/2.54 331 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(B,A),C,A) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A) | -c_lessequals(B,C,A) # label(cls_abs__le__iff_2) # label(axiom). [assumption].
% 2.26/2.54 332 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Oabs__class_Oabs(B,A) # label(cls_abs__minus__cancel_0) # label(axiom). [assumption].
% 2.26/2.54 333 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__le__zero__iff_1) # label(axiom). [assumption].
% 2.26/2.54 334 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = c_HOL_Ouminus__class_Ouminus(B,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__of__nonpos_0) # label(axiom). [assumption].
% 2.26/2.54 335 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(B,A),A) = c_HOL_Oabs__class_Oabs(B,A) # label(cls_abs__idempotent_0) # label(axiom). [assumption].
% 2.26/2.54 336 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oabs__class_Oabs(B,A),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_zero__less__abs__iff_1) # label(axiom). [assumption].
% 2.26/2.54 337 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),c_HOL_Oabs__class_Oabs(B,A),A) # label(cls_abs__ge__minus__self_0) # label(axiom). [assumption].
% 2.26/2.54 338 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(B,c_HOL_Oabs__class_Oabs(B,A),A) # label(cls_abs__ge__self_0) # label(axiom). [assumption].
% 2.26/2.54 339 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__not__less__zero_0) # label(axiom). [assumption].
% 2.26/2.54 340 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oabs__class_Oabs(B,A)),c_HOL_Oabs__class_Oabs(C,A)),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oabs__class_Oabs(B,A)),c_HOL_Oabs__class_Oabs(C,A)) # label(cls_abs__add__abs_0) # label(axiom). [assumption].
% 2.26/2.54 341 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_abs__eq__0_0) # label(axiom). [assumption].
% 2.26/2.54 342 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(A),A),A) # label(cls_zero__less__abs__iff_0) # label(axiom). [assumption].
% 2.26/2.54 343 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Oabs__class_Oabs(B,A),A) # label(cls_abs__ge__zero_0) # label(axiom). [assumption].
% 2.26/2.58 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(320,a,321,a)].
% 2.26/2.58 Derived: c_HOL_Oabs__class_Oabs(A,tc_Int_Oint) = A | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(320,a,322,a)].
% 2.26/2.58 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),B,tc_Int_Oint). [resolve(320,a,323,a)].
% 2.26/2.58 Derived: c_HOL_Oabs__class_Oabs(A,tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(320,a,324,a)].
% 2.26/2.58 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(320,a,325,a)].
% 2.26/2.58 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),B,tc_Int_Oint). [resolve(320,a,326,a)].
% 2.26/2.58 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(320,a,327,a)].
% 2.26/2.58 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Oabs__class_Oabs(A,tc_Int_Oint)),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint)),tc_Int_Oint). [resolve(320,a,328,a)].
% 2.26/2.58 Derived: c_HOL_Oabs__class_Oabs(A,tc_Int_Oint) = A | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(320,a,329,a)].
% 2.26/2.58 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(320,a,330,a)].
% 2.26/2.58 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oabs__class_Oabs(A,tc_Int_Oint). [resolve(320,a,332,a)].
% 2.26/2.58 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(320,a,333,a)].
% 2.26/2.58 Derived: c_HOL_Oabs__class_Oabs(A,tc_Int_Oint) = c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(320,a,334,a)].
% 2.26/2.58 Derived: c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),tc_Int_Oint) = c_HOL_Oabs__class_Oabs(A,tc_Int_Oint). [resolve(320,a,335,a)].
% 2.26/2.58 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(320,a,336,a)].
% 2.26/2.58 Derived: c_lessequals(c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint),c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),tc_Int_Oint). [resolve(320,a,337,a)].
% 2.26/2.58 Derived: c_lessequals(A,c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),tc_Int_Oint). [resolve(320,a,338,a)].
% 2.26/2.58 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(320,a,339,a)].
% 2.26/2.58 Derived: c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Oabs__class_Oabs(A,tc_Int_Oint)),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint)),tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Oabs__class_Oabs(A,tc_Int_Oint)),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint)). [resolve(320,a,340,a)].
% 2.26/2.58 Derived: c_HOL_Oabs__class_Oabs(A,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(320,a,341,a)].
% 2.26/2.58 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(320,a,342,a)].
% 2.26/2.58 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oabs__class_Oabs(A,tc_Int_Oint),tc_Int_Oint). [resolve(320,a,343,a)].
% 2.26/2.58 344 class_OrderedGroup_Olordered__ab__group__add__abs(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__abs) # label(axiom). [assumption].
% 2.33/2.66 345 -class_OrderedGroup_Olordered__ab__group__add__abs(A) | c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),c_HOL_Oabs__class_Oabs(D,A)),A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A) # label(cls_estimate__by__abs_0) # label(axiom). [assumption].
% 2.33/2.66 346 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = c_HOL_Ouminus__class_Ouminus(B,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if__lattice_0) # label(axiom). [assumption].
% 2.33/2.66 347 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add__abs(A) | c_HOL_Oabs__class_Oabs(B,A) = B | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if__lattice_1) # label(axiom). [assumption].
% 2.33/2.66 Derived: c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),c_HOL_Oabs__class_Oabs(C,tc_Int_Oint)),tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C),B,tc_Int_Oint). [resolve(344,a,345,a)].
% 2.33/2.66 Derived: -class_Orderings_Olinorder(tc_Int_Oint) | c_HOL_Oabs__class_Oabs(A,tc_Int_Oint) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(344,a,347,b)].
% 2.33/2.66 348 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 2.33/2.66 349 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_lessequals(C,D,A) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 2.33/2.66 350 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_lessequals(B,D,A) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 2.33/2.66 351 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__mono_0) # label(axiom). [assumption].
% 2.33/2.66 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(348,a,349,a)].
% 2.33/2.66 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(348,a,350,a)].
% 2.33/2.66 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(348,a,351,a)].
% 2.33/2.66 352 class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 2.33/2.66 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C),tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint). [resolve(352,a,349,a)].
% 2.33/2.66 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),B),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(352,a,350,a)].
% 2.33/2.66 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),D),tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(352,a,351,a)].
% 2.33/2.66 353 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 2.33/2.66 354 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) # label(cls_add__le__cancel__left_0) # label(axiom). [assumption].
% 2.33/2.66 355 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_lessequals(C,D,A) # label(cls_add__le__cancel__left_1) # label(axiom). [assumption].
% 2.33/2.66 356 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_add__le__cancel__right_0) # label(axiom). [assumption].
% 2.33/2.66 357 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_lessequals(B,D,A) # label(cls_add__le__cancel__right_1) # label(axiom). [assumption].
% 2.33/2.66 358 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) # label(cls_add__increasing2_0) # label(axiom). [assumption].
% 2.33/2.66 359 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__increasing_0) # label(axiom). [assumption].
% 2.33/2.66 360 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__strict__increasing2_0) # label(axiom). [assumption].
% 2.33/2.66 361 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__cancel__right_1) # label(axiom). [assumption].
% 2.33/2.66 362 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_add__less__cancel__right_0) # label(axiom). [assumption].
% 2.33/2.66 363 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__less__cancel__left_1) # label(axiom). [assumption].
% 2.33/2.66 364 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) # label(cls_add__less__cancel__left_0) # label(axiom). [assumption].
% 2.33/2.66 365 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_lessequals(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_add__strict__increasing_0) # label(axiom). [assumption].
% 2.33/2.66 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat). [resolve(353,a,354,a)].
% 2.33/2.66 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat). [resolve(353,a,356,a)].
% 2.33/2.66 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat). [resolve(353,a,358,a)].
% 2.33/2.66 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(353,a,359,a)].
% 2.33/2.66 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(353,a,360,a)].
% 2.41/2.71 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(353,a,361,a)].
% 2.41/2.71 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat). [resolve(353,a,362,a)].
% 2.41/2.71 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(353,a,363,a)].
% 2.41/2.71 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat). [resolve(353,a,364,a)].
% 2.41/2.71 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_nat) | c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(353,a,365,a)].
% 2.41/2.71 366 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 2.41/2.71 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),B),tc_Int_Oint). [resolve(366,a,354,a)].
% 2.41/2.71 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C),tc_Int_Oint). [resolve(366,a,356,a)].
% 2.41/2.71 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C),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(366,a,358,a)].
% 2.41/2.71 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C),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(366,a,359,a)].
% 2.41/2.71 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C),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(366,a,360,a)].
% 2.41/2.71 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),B),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(366,a,361,a)].
% 2.41/2.71 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C),tc_Int_Oint). [resolve(366,a,362,a)].
% 2.41/2.71 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,C,tc_Int_Oint). [resolve(366,a,363,a)].
% 2.41/2.71 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),B),tc_Int_Oint). [resolve(366,a,364,a)].
% 2.41/2.71 Derived: -class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) | c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C),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(366,a,365,a)].
% 2.41/2.71 367 class_Ring__and__Field_Opordered__ring__abs(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs) # label(axiom). [assumption].
% 2.41/2.75 368 -class_Ring__and__Field_Opordered__ring__abs(A) | c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oabs__class_Oabs(B,A)),c_HOL_Oabs__class_Oabs(C,A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__eq__mult_0) # label(axiom). [assumption].
% 2.41/2.75 369 -class_Ring__and__Field_Opordered__ring__abs(A) | c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oabs__class_Oabs(B,A)),c_HOL_Oabs__class_Oabs(C,A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__eq__mult_1) # label(axiom). [assumption].
% 2.41/2.75 370 -class_Ring__and__Field_Opordered__ring__abs(A) | c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oabs__class_Oabs(B,A)),c_HOL_Oabs__class_Oabs(C,A)) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__eq__mult_2) # label(axiom). [assumption].
% 2.41/2.75 371 -class_Ring__and__Field_Opordered__ring__abs(A) | c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oabs__class_Oabs(B,A)),c_HOL_Oabs__class_Oabs(C,A)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__eq__mult_3) # label(axiom). [assumption].
% 2.41/2.75 372 class_Ring__and__Field_Oring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring) # label(axiom). [assumption].
% 2.41/2.75 373 -class_Ring__and__Field_Oring(A) | c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ouminus__class_Ouminus(B,A)),C) # label(cls_minus__mult__left_0) # label(axiom). [assumption].
% 2.41/2.75 374 -class_Ring__and__Field_Oring(A) | c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ouminus__class_Ouminus(C,A)) # label(cls_minus__mult__right_0) # label(axiom). [assumption].
% 2.41/2.75 375 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ouminus__class_Ouminus(B,A)),c_HOL_Ouminus__class_Ouminus(C,A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) # label(cls_minus__mult__minus_0) # label(axiom). [assumption].
% 2.41/2.75 376 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ouminus__class_Ouminus(B,A)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ouminus__class_Ouminus(C,A)) # label(cls_minus__mult__commute_0) # label(axiom). [assumption].
% 2.41/2.75 Derived: c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint)),B). [resolve(372,a,373,a)].
% 2.41/2.75 Derived: c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint)). [resolve(372,a,374,a)].
% 2.41/2.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint)),c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B). [resolve(372,a,375,a)].
% 2.41/2.75 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint)). [resolve(372,a,376,a)].
% 2.41/2.75 377 class_Ring__and__Field_Oring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring) # label(axiom). [assumption].
% 2.41/2.75 Derived: c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),B). [resolve(377,a,373,a)].
% 2.41/2.75 Derived: c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex)). [resolve(377,a,374,a)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B). [resolve(377,a,375,a)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex)). [resolve(377,a,376,a)].
% 2.53/2.81 378 c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(tc_nat),c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(271,a,298,a)].
% 2.53/2.81 379 hAPP(hAPP(A,B),hAPP(hAPP(C,B),D)) = hAPP(hAPP(C,B),c_Suc(D)) | -c_Groebner__Basis_Ogb__semiring(E,A,C,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I27_J_0) # label(axiom). [assumption].
% 2.53/2.81 380 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),C) = hAPP(hAPP(B,C),c_Suc(D)) | -c_Groebner__Basis_Ogb__semiring(E,A,B,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I28_J_0) # label(axiom). [assumption].
% 2.53/2.81 381 hAPP(hAPP(A,B),c_Suc(C)) = hAPP(hAPP(D,B),hAPP(hAPP(A,B),C)) | -c_Groebner__Basis_Ogb__semiring(E,D,A,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I35_J_0) # label(axiom). [assumption].
% 2.53/2.81 382 hAPP(hAPP(A,B),c_Suc(C)) = hAPP(hAPP(D,B),hAPP(hAPP(A,B),C)) | -c_Groebner__Basis_Ogb__semiring(E,D,A,F,V6,V7) # label(cls_gb__semiring_Opwr__Suc_0) # label(axiom). [assumption].
% 2.53/2.81 383 hAPP(hAPP(A,B),c_HOL_Ozero__class_Ozero(tc_nat)) = C | -c_Groebner__Basis_Ogb__semiring(D,E,A,F,C,V6) # label(cls_gb__semiring_Opwr__0_0) # label(axiom). [assumption].
% 2.53/2.81 384 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),hAPP(hAPP(B,E),D)) = hAPP(hAPP(B,hAPP(hAPP(A,C),E)),D) | -c_Groebner__Basis_Ogb__semiring(A,B,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I1_J_0) # label(axiom). [assumption].
% 2.53/2.81 385 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),D) = hAPP(hAPP(B,hAPP(hAPP(A,C),E)),D) | -c_Groebner__Basis_Ogb__semiring(A,B,F,V6,E,V7) # label(cls_gb__semiring_Osemiring__rules_I2_J_0) # label(axiom). [assumption].
% 2.53/2.81 386 hAPP(hAPP(A,B),hAPP(hAPP(C,D),B)) = hAPP(hAPP(C,hAPP(hAPP(A,D),E)),B) | -c_Groebner__Basis_Ogb__semiring(A,C,F,V6,E,V7) # label(cls_gb__semiring_Osemiring__rules_I3_J_0) # label(axiom). [assumption].
% 2.53/2.81 387 hAPP(hAPP(A,B),B) = hAPP(hAPP(C,hAPP(hAPP(A,D),D)),B) | -c_Groebner__Basis_Ogb__semiring(A,C,E,F,D,V6) # label(cls_gb__semiring_Osemiring__rules_I4_J_0) # label(axiom). [assumption].
% 2.53/2.81 388 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(A,D,E,B,F,V6) # label(cls_gb__semiring_Osemiring__rules_I5_J_0) # label(axiom). [assumption].
% 2.53/2.81 389 hAPP(hAPP(A,B),C) = B | -c_Groebner__Basis_Ogb__semiring(A,D,E,C,F,V6) # label(cls_gb__semiring_Osemiring__rules_I6_J_0) # label(axiom). [assumption].
% 2.53/2.81 390 hAPP(hAPP(A,B),C) = hAPP(hAPP(A,C),B) | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I7_J_0) # label(axiom). [assumption].
% 2.53/2.81 391 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),E) = hAPP(hAPP(B,hAPP(hAPP(A,C),E)),hAPP(hAPP(A,D),E)) | -c_Groebner__Basis_Ogb__semiring(B,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I8_J_0) # label(axiom). [assumption].
% 2.53/2.81 392 hAPP(hAPP(A,B),C) = B | -c_Groebner__Basis_Ogb__semiring(D,A,E,B,F,V6) # label(cls_gb__semiring_Osemiring__rules_I9_J_0) # label(axiom). [assumption].
% 2.53/2.81 393 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(D,A,E,C,F,V6) # label(cls_gb__semiring_Osemiring__rules_I10_J_0) # label(axiom). [assumption].
% 2.53/2.81 394 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,B,V6) # label(cls_gb__semiring_Osemiring__rules_I11_J_0) # label(axiom). [assumption].
% 2.53/2.81 395 hAPP(hAPP(A,B),C) = B | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,C,V6) # label(cls_gb__semiring_Osemiring__rules_I12_J_0) # label(axiom). [assumption].
% 2.53/2.81 396 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E)) = hAPP(hAPP(A,hAPP(hAPP(A,B),D)),hAPP(hAPP(A,C),E)) | -c_Groebner__Basis_Ogb__semiring(F,A,V6,V7,V8,V9) # label(cls_gb__semiring_Osemiring__rules_I13_J_0) # label(axiom). [assumption].
% 2.53/2.81 397 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E)) = hAPP(hAPP(A,B),hAPP(hAPP(A,C),hAPP(hAPP(A,D),E))) | -c_Groebner__Basis_Ogb__semiring(F,A,V6,V7,V8,V9) # label(cls_gb__semiring_Osemiring__rules_I14_J_0) # label(axiom). [assumption].
% 2.53/2.81 398 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E)) = hAPP(hAPP(A,D),hAPP(hAPP(A,hAPP(hAPP(A,B),C)),E)) | -c_Groebner__Basis_Ogb__semiring(F,A,V6,V7,V8,V9) # label(cls_gb__semiring_Osemiring__rules_I15_J_0) # label(axiom). [assumption].
% 2.53/2.81 399 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,hAPP(hAPP(A,B),D)),C) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I16_J_0) # label(axiom). [assumption].
% 2.53/2.81 400 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I17_J_0) # label(axiom). [assumption].
% 2.53/2.81 401 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I18_J_0) # label(axiom). [assumption].
% 2.53/2.81 402 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,C),hAPP(hAPP(A,B),D)) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I19_J_0) # label(axiom). [assumption].
% 2.53/2.81 403 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E)) = hAPP(hAPP(A,hAPP(hAPP(A,B),D)),hAPP(hAPP(A,C),E)) | -c_Groebner__Basis_Ogb__semiring(A,F,V6,V7,V8,V9) # label(cls_gb__semiring_Osemiring__rules_I20_J_0) # label(axiom). [assumption].
% 2.53/2.81 404 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I21_J_0) # label(axiom). [assumption].
% 2.53/2.81 405 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,C),hAPP(hAPP(A,B),D)) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I22_J_0) # label(axiom). [assumption].
% 2.53/2.81 406 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,hAPP(hAPP(A,B),D)),C) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I23_J_0) # label(axiom). [assumption].
% 2.53/2.81 407 hAPP(hAPP(A,B),C) = hAPP(hAPP(A,C),B) | -c_Groebner__Basis_Ogb__semiring(A,D,E,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I24_J_0) # label(axiom). [assumption].
% 2.53/2.81 408 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I25_J_0) # label(axiom). [assumption].
% 2.53/2.81 409 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(A,D,E,B,F,V6) # label(cls_gb__semiring_Oadd__0_0) # label(axiom). [assumption].
% 2.53/2.81 410 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Oadd__a_0) # label(axiom). [assumption].
% 2.53/2.81 411 hAPP(hAPP(A,B),C) = hAPP(hAPP(A,C),B) | -c_Groebner__Basis_Ogb__semiring(A,D,E,F,V6,V7) # label(cls_gb__semiring_Oadd__c_0) # label(axiom). [assumption].
% 2.53/2.81 412 hAPP(hAPP(A,B),C) = B | -c_Groebner__Basis_Ogb__semiring(D,A,E,B,F,V6) # label(cls_gb__semiring_Omul__0_0) # label(axiom). [assumption].
% 2.53/2.81 413 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,B,V6) # label(cls_gb__semiring_Omul__1_0) # label(axiom). [assumption].
% 2.53/2.81 414 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Omul__a_0) # label(axiom). [assumption].
% 2.53/2.81 415 hAPP(hAPP(A,B),C) = hAPP(hAPP(A,C),B) | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,V6,V7) # label(cls_gb__semiring_Omul__c_0) # label(axiom). [assumption].
% 2.53/2.81 416 hAPP(hAPP(A,B),hAPP(hAPP(C,D),E)) = hAPP(hAPP(C,hAPP(hAPP(A,B),D)),hAPP(hAPP(A,B),E)) | -c_Groebner__Basis_Ogb__semiring(C,A,F,V6,V7,V8) # label(cls_gb__semiring_Omul__d_0) # label(axiom). [assumption].
% 2.53/2.81 417 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),E) = hAPP(hAPP(B,hAPP(hAPP(A,C),E)),hAPP(hAPP(A,D),E)) | -c_Groebner__Basis_Ogb__semiring(F,B,A,V6,V7,V8) # label(cls_gb__semiring_Opwr__mul_0) # label(axiom). [assumption].
% 2.53/2.81 418 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) | -c_Groebner__Basis_Ogb__semiring(E,F,A,V6,V7,V8) # label(cls_gb__semiring_Opwr__pwr_0) # label(axiom). [assumption].
% 2.53/2.81 419 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),hAPP(hAPP(B,C),E)) = hAPP(hAPP(B,C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),E)) | -c_Groebner__Basis_Ogb__semiring(F,A,B,V6,V7,V8) # label(cls_gb__semiring_Omul__pwr_0) # label(axiom). [assumption].
% 2.53/2.81 420 hAPP(hAPP(A,B),c_HOL_Oone__class_Oone(tc_nat)) = B | -c_Groebner__Basis_Ogb__semiring(C,D,A,E,F,V6) # label(cls_gb__semiring_Osemiring__rules_I33_J_0) # label(axiom). [assumption].
% 2.53/2.81 421 hAPP(hAPP(A,B),c_Suc(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C))) = hAPP(hAPP(D,B),hAPP(hAPP(D,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,B),C))) | -c_Groebner__Basis_Ogb__semiring(E,D,A,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I37_J_0) # label(axiom). [assumption].
% 2.53/2.81 422 hAPP(hAPP(A,B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C)) = hAPP(hAPP(D,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,B),C)) | -c_Groebner__Basis_Ogb__semiring(E,D,A,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I36_J_0) # label(axiom). [assumption].
% 2.53/2.81 423 hAPP(hAPP(A,B),B) = hAPP(hAPP(C,B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) | -c_Groebner__Basis_Ogb__semiring(D,A,C,E,F,V6) # label(cls_gb__semiring_Osemiring__rules_I29_J_0) # label(axiom). [assumption].
% 2.53/2.81 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)). [resolve(378,a,381,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat). [resolve(378,a,383,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B). [resolve(378,a,384,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(378,a,390,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(378,a,391,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = A. [resolve(378,a,394,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(378,a,395,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),D)). [resolve(378,a,396,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))). [resolve(378,a,397,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),D)). [resolve(378,a,398,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),B). [resolve(378,a,399,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(378,a,400,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C). [resolve(378,a,401,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)). [resolve(378,a,402,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),D)). [resolve(378,a,403,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(378,a,404,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)). [resolve(378,a,405,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B). [resolve(378,a,406,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C). [resolve(378,a,408,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)). [resolve(378,a,416,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(378,a,419,b)].
% 2.53/2.81 424 c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(318,a,298,a)].
% 2.53/2.81 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)). [resolve(424,a,381,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(424,a,383,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C)),B). [resolve(424,a,384,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A). [resolve(424,a,390,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)). [resolve(424,a,391,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(424,a,392,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(424,a,393,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),A) = A. [resolve(424,a,394,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(424,a,395,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D)). [resolve(424,a,396,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))). [resolve(424,a,397,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),D)). [resolve(424,a,398,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)),B). [resolve(424,a,399,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)). [resolve(424,a,400,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C). [resolve(424,a,401,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)). [resolve(424,a,402,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),D)). [resolve(424,a,403,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)). [resolve(424,a,404,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C)). [resolve(424,a,405,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C)),B). [resolve(424,a,406,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),C). [resolve(424,a,408,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)). [resolve(424,a,416,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(424,a,419,b)].
% 2.53/2.81 425 c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(319,a,298,a)].
% 2.53/2.81 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)). [resolve(425,a,381,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(425,a,383,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)),B). [resolve(425,a,384,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A). [resolve(425,a,390,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)). [resolve(425,a,391,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(425,a,392,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(425,a,393,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A) = A. [resolve(425,a,394,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(425,a,395,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)). [resolve(425,a,396,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D))). [resolve(425,a,397,b)].
% 2.53/2.81 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),D)). [resolve(425,a,398,b)].
% 2.56/2.84 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),B). [resolve(425,a,399,b)].
% 2.56/2.84 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)). [resolve(425,a,400,b)].
% 2.56/2.84 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),C). [resolve(425,a,401,b)].
% 2.56/2.84 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)). [resolve(425,a,402,b)].
% 2.56/2.84 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),D)). [resolve(425,a,403,b)].
% 2.56/2.84 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)). [resolve(425,a,404,b)].
% 2.56/2.84 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)). [resolve(425,a,405,b)].
% 2.56/2.84 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)),B). [resolve(425,a,406,b)].
% 2.56/2.84 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),C). [resolve(425,a,408,b)].
% 2.56/2.84 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)). [resolve(425,a,416,b)].
% 2.56/2.84 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(425,a,419,b)].
% 2.56/2.84 426 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 2.56/2.84 427 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A)),A) # label(cls_less__add__one_0) # label(axiom). [assumption].
% 2.56/2.84 428 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_HOL_Oord__class_Oless(B,D,A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 2.56/2.84 429 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A)),A) # label(cls_zero__less__two_0) # label(axiom). [assumption].
% 2.56/2.84 430 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(B,D,A) # label(cls_power__mono_0) # label(axiom). [assumption].
% 2.56/2.84 431 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)) != hAPP(hAPP(c_Power_Opower__class_Opower(A),D),c_Suc(C)) | B = D | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__inject__base_0) # label(axiom). [assumption].
% 2.56/2.84 432 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__Suc__less_0) # label(axiom). [assumption].
% 2.56/2.84 433 -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].
% 2.56/2.84 434 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C) | 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].
% 2.56/2.84 435 -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].
% 2.56/2.84 436 -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].
% 2.56/2.84 437 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),C,A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_less__1__mult_0) # label(axiom). [assumption].
% 2.56/2.84 438 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)),c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power__Suc__less__one_0) # label(axiom). [assumption].
% 2.56/2.84 439 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__le__power_0) # label(axiom). [assumption].
% 2.56/2.84 440 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_lessequals(c_HOL_Oone__class_Oone(A),B,A) # label(cls_one__le__power_0) # label(axiom). [assumption].
% 2.56/2.84 441 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__gt1_0) # label(axiom). [assumption].
% 2.56/2.84 442 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__less__power__Suc_0) # label(axiom). [assumption].
% 2.56/2.84 443 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) # label(cls_power__gt1__lemma_0) # label(axiom). [assumption].
% 2.56/2.84 444 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D),A) # label(cls_power__less__imp__less__base_0) # label(axiom). [assumption].
% 2.56/2.84 445 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),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].
% 2.56/2.84 446 -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].
% 2.56/2.84 447 -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].
% 2.56/2.84 448 -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].
% 2.56/2.84 449 -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].
% 2.56/2.84 450 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Suc(D)),A) # label(cls_power__le__imp__le__base_0) # label(axiom). [assumption].
% 2.56/2.84 451 -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].
% 2.56/2.84 452 -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].
% 2.56/2.84 453 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),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].
% 2.56/2.84 454 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),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].
% 2.56/2.84 455 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A) | C = D # label(cls_power__inject__exp_0) # label(axiom). [assumption].
% 2.56/2.84 456 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_zero__less__power_0) # label(axiom). [assumption].
% 2.56/2.84 457 -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].
% 2.56/2.84 458 -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].
% 2.56/2.84 459 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A) # label(cls_power2__le__imp__le_0) # label(axiom). [assumption].
% 2.56/2.84 460 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) != hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) | B = C | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_power2__eq__imp__eq_0) # label(axiom). [assumption].
% 2.56/2.84 461 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A) # label(cls_power__strict__increasing__iff_0) # label(axiom). [assumption].
% 2.56/2.84 462 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),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].
% 2.56/2.84 463 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),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].
% 2.56/2.84 464 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),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].
% 2.56/2.84 465 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A) # label(cls_power2__less__imp__less_0) # label(axiom). [assumption].
% 2.56/2.84 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),tc_nat). [resolve(426,a,427,a)].
% 2.56/2.84 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). [resolve(426,a,428,a)].
% 2.56/2.84 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat). [resolve(426,a,429,a)].
% 2.56/2.84 Derived: c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(426,a,430,a)].
% 2.56/2.84 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),c_Suc(B)) | A = C | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(426,a,431,a)].
% 2.56/2.84 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(426,a,432,a)].
% 2.56/2.84 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(426,a,433,a)].
% 2.56/2.84 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B) | 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(426,a,434,a)].
% 2.56/2.84 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat). [resolve(426,a,435,a)].
% 2.56/2.84 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(426,a,437,a)].
% 2.56/2.84 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(426,a,438,a)].
% 2.56/2.84 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(426,a,439,a)].
% 2.56/2.84 Derived: c_lessequals(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat) | -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(426,a,440,a)].
% 2.56/2.84 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(426,a,441,a)].
% 2.56/2.84 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(426,a,442,a)].
% 2.56/2.84 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(426,a,443,a)].
% 2.56/2.84 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),C),tc_nat). [resolve(426,a,444,a)].
% 2.56/2.84 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B),tc_nat) | -c_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(426,a,445,a)].
% 2.56/2.84 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(426,a,446,a)].
% 2.56/2.84 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(426,a,447,a)].
% 2.56/2.84 Derived: -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(426,a,448,a)].
% 2.56/2.84 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(426,a,449,a)].
% 2.56/2.84 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),c_Suc(C)),tc_nat). [resolve(426,a,450,a)].
% 2.56/2.84 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(426,a,451,a)].
% 2.56/2.84 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(426,a,452,a)].
% 2.56/2.84 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C),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(426,a,453,a)].
% 2.56/2.84 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(426,a,454,a)].
% 2.56/2.84 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) | B = C. [resolve(426,a,455,a)].
% 2.56/2.84 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(426,a,456,a)].
% 2.56/2.84 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(426,a,457,a)].
% 2.56/2.84 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(426,a,458,a)].
% 2.56/2.84 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_nat). [resolve(426,a,459,a)].
% 2.56/2.84 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) | A = B | -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(426,a,460,a)].
% 2.56/2.84 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),C,tc_nat). [resolve(426,a,461,a)].
% 2.56/2.84 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C),tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(426,a,463,a)].
% 2.56/2.84 466 class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 2.56/2.84 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint)),tc_Int_Oint). [resolve(466,a,427,a)].
% 2.56/2.84 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C),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(466,a,428,a)].
% 2.56/2.85 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),c_HOL_Oone__class_Oone(tc_Int_Oint)),tc_Int_Oint). [resolve(466,a,429,a)].
% 2.56/2.85 Derived: c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B),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(466,a,430,a)].
% 2.56/2.85 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Suc(B)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),c_Suc(B)) | 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(466,a,431,a)].
% 2.56/2.85 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),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(466,a,432,a)].
% 2.56/2.85 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(466,a,433,a)].
% 2.56/2.85 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B) | 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(466,a,434,a)].
% 2.56/2.85 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(466,a,435,a)].
% 2.56/2.85 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),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(466,a,437,a)].
% 2.56/2.85 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Suc(B)),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(466,a,438,a)].
% 2.56/2.85 Derived: c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint) | -c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(466,a,440,a)].
% 2.56/2.85 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Suc(B)),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(466,a,441,a)].
% 2.56/2.85 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(466,a,442,a)].
% 2.56/2.85 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(466,a,443,a)].
% 2.56/2.85 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(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C),tc_Int_Oint). [resolve(466,a,444,a)].
% 2.56/2.85 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B),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(466,a,445,a)].
% 2.56/2.85 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(466,a,446,a)].
% 2.56/2.85 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(466,a,447,a)].
% 2.56/2.85 Derived: -c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(466,a,448,a)].
% 2.56/2.85 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(466,a,449,a)].
% 2.56/2.85 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Suc(C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Suc(C)),tc_Int_Oint). [resolve(466,a,450,a)].
% 2.56/2.85 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(466,a,451,a)].
% 2.56/2.85 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(466,a,452,a)].
% 2.56/2.85 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C),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(466,a,453,a)].
% 2.56/2.85 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),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(466,a,454,a)].
% 2.56/2.85 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint) | B = C. [resolve(466,a,455,a)].
% 2.56/2.85 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(466,a,456,a)].
% 2.56/2.85 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(466,a,457,a)].
% 2.56/2.85 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(466,a,458,a)].
% 2.56/2.85 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_Int_Oint). [resolve(466,a,459,a)].
% 2.56/2.85 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) | A = B | -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(466,a,460,a)].
% 2.56/2.85 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),C,tc_Int_Oint). [resolve(466,a,461,a)].
% 2.66/2.93 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(466,a,463,a)].
% 2.66/2.93 467 class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 2.66/2.93 468 -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].
% 2.66/2.93 469 -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].
% 2.66/2.93 470 -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].
% 2.66/2.93 471 -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].
% 2.66/2.93 472 -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].
% 2.66/2.93 473 -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].
% 2.66/2.93 474 -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].
% 2.66/2.93 475 -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].
% 2.66/2.93 476 -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].
% 2.66/2.93 477 -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].
% 2.66/2.93 478 -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].
% 2.66/2.93 479 -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].
% 2.66/2.93 480 -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].
% 2.66/2.93 481 -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].
% 2.66/2.93 482 -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].
% 2.66/2.93 483 -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].
% 2.66/2.93 484 -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].
% 2.66/2.93 485 -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].
% 2.66/2.93 486 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_lessequals(E,D,A) | -c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E),A) # label(cls_le__add__right__mono_0) # label(axiom). [assumption].
% 2.66/2.93 487 -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].
% 2.66/2.93 488 -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].
% 2.66/2.93 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(467,a,468,a)].
% 2.66/2.93 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(467,a,469,a)].
% 2.66/2.93 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(467,a,470,a)].
% 2.66/2.93 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(467,a,471,a)].
% 2.66/2.93 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(467,a,472,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_Ouminus__class_Ouminus(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(467,a,473,a)].
% 2.66/2.93 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(467,a,474,a)].
% 2.66/2.93 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(467,a,476,a)].
% 2.66/2.93 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(467,a,478,a)].
% 2.66/2.93 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(467,a,479,a)].
% 2.66/2.93 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(467,a,480,a)].
% 2.66/2.93 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(467,a,481,a)].
% 2.66/2.97 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(467,a,482,a)].
% 2.66/2.97 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(467,a,484,a)].
% 2.66/2.97 Derived: c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C),tc_Int_Oint) | -c_lessequals(D,C,tc_Int_Oint) | -c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),D),tc_Int_Oint). [resolve(467,a,486,a)].
% 2.66/2.97 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(467,a,487,a)].
% 2.66/2.97 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(467,a,488,a)].
% 2.66/2.97 489 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 2.66/2.97 490 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__0__left_1) # label(axiom). [assumption].
% 2.66/2.97 491 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Suc(B)) = c_HOL_Ozero__class_Ozero(A) # label(cls_power__0__Suc_0) # label(axiom). [assumption].
% 2.66/2.97 492 -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) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat)) = c_HOL_Oone__class_Oone(A) # label(cls_power__0__left__number__of_0) # label(axiom). [assumption].
% 2.66/2.97 493 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(A) # label(cls_power__0__left_0) # label(axiom). [assumption].
% 2.66/2.97 494 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat)) = 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].
% 2.66/2.97 Derived: -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(489,a,490,a)].
% 2.66/2.97 Derived: -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(A)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(489,a,491,a)].
% 2.66/2.97 Derived: -class_Power_Opower(tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Oone__class_Oone(tc_nat). [resolve(489,a,492,a)].
% 2.66/2.97 495 class_Ring__and__Field_Osemiring__0(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 2.66/2.97 Derived: -class_Power_Opower(tc_Int_Oint) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(495,a,490,a)].
% 2.66/2.97 Derived: -class_Power_Opower(tc_Int_Oint) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Suc(A)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(495,a,491,a)].
% 2.82/3.09 Derived: -class_Power_Opower(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(495,a,492,a)].
% 2.82/3.09 496 class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 2.82/3.09 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(496,a,490,a)].
% 2.82/3.09 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_Suc(A)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(496,a,491,a)].
% 2.82/3.09 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(A,tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(496,a,492,a)].
% 2.82/3.09 497 class_Ring__and__Field_Omult__mono1(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 2.82/3.09 498 -class_Ring__and__Field_Omult__mono1(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,D,A) # label(cls_mult__mono1_0) # label(axiom). [assumption].
% 2.82/3.09 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(497,a,498,a)].
% 2.82/3.09 499 class_Ring__and__Field_Omult__mono1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 2.82/3.09 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),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(499,a,498,a)].
% 2.82/3.09 500 class_Ring__and__Field_Omult__mono(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 2.82/3.09 501 -class_Ring__and__Field_Omult__mono(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,D,A) # label(cls_mult__left__mono_0) # label(axiom). [assumption].
% 2.82/3.09 502 -class_Ring__and__Field_Omult__mono(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,D,A) # label(cls_mult__right__mono_0) # label(axiom). [assumption].
% 2.82/3.09 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(500,a,502,a)].
% 2.82/3.09 503 class_Ring__and__Field_Omult__mono(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 2.82/3.09 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),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(503,a,502,a)].
% 2.82/3.09 504 class_Ring__and__Field_Opordered__ring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 2.82/3.17 505 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(D,C,A) # label(cls_mult__left__mono__neg_0) # label(axiom). [assumption].
% 2.82/3.17 506 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(D,B,A) # label(cls_mult__right__mono__neg_0) # label(axiom). [assumption].
% 2.82/3.17 507 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_split__mult__pos__le_0) # label(axiom). [assumption].
% 2.82/3.17 508 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_split__mult__pos__le_1) # label(axiom). [assumption].
% 2.82/3.17 509 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__nonpos__nonpos_0) # label(axiom). [assumption].
% 2.82/3.17 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),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(504,a,505,a)].
% 2.82/3.17 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B),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(504,a,506,a)].
% 2.82/3.17 510 class_Ring__and__Field_Oabs__if(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oabs__if) # label(axiom). [assumption].
% 2.82/3.17 511 -class_Ring__and__Field_Oabs__if(A) | c_HOL_Oabs__class_Oabs(B,A) = c_HOL_Ouminus__class_Ouminus(B,A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if_0) # label(axiom). [assumption].
% 2.82/3.17 512 -class_Ring__and__Field_Oabs__if(A) | c_HOL_Oabs__class_Oabs(B,A) = B | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if_1) # label(axiom). [assumption].
% 2.82/3.17 Derived: c_HOL_Oabs__class_Oabs(A,tc_Int_Oint) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(510,a,512,a)].
% 2.82/3.17 513 class_Ring__and__Field_Oidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 2.82/3.17 514 -class_Ring__and__Field_Oidom(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),C) | B = c_HOL_Ouminus__class_Ouminus(C,A) | B = C # label(cls_square__eq__iff_0) # label(axiom). [assumption].
% 2.82/3.17 515 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__r0__iff_0) # label(axiom). [assumption].
% 2.82/3.17 516 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) # label(cls_class__ringb_Oadd__mul__solve_1) # label(axiom). [assumption].
% 2.82/3.17 517 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) # label(cls_class__ringb_Onoteq__reduce_1) # label(axiom). [assumption].
% 2.82/3.17 518 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) | D = E | C = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Oadd__scale__eq__noteq_0) # label(axiom). [assumption].
% 2.82/3.17 519 -class_Ring__and__Field_Oidom(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ouminus__class_Ouminus(B,A)),c_HOL_Ouminus__class_Ouminus(B,A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B) # label(cls_square__eq__iff_1) # label(axiom). [assumption].
% 2.82/3.17 520 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_class__ringb_Oadd__cancel_0) # label(axiom). [assumption].
% 2.82/3.17 521 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | B = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) # label(cls_class__ringb_Oadd__r0__iff_1) # label(axiom). [assumption].
% 2.82/3.17 522 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)) | C = E | B = D # label(cls_class__ringb_Onoteq__reduce_0) # label(axiom). [assumption].
% 2.82/3.17 523 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)) | C = E | B = D # label(cls_class__ringb_Oadd__mul__solve_0) # label(axiom). [assumption].
% 2.82/3.17 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),B) | A = c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint) | A = B. [resolve(513,a,514,a)].
% 2.82/3.17 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | A != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(513,a,515,a)].
% 2.82/3.17 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D)) | C = D | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(513,a,518,a)].
% 2.82/3.17 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C) | B = C. [resolve(513,a,520,a)].
% 2.82/3.17 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)). [resolve(513,a,521,a)].
% 2.82/3.17 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B)) | B = D | A = C. [resolve(513,a,522,a)].
% 2.82/3.17 524 class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 2.82/3.17 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),A) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),B) | A = c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex) | A = B. [resolve(524,a,514,a)].
% 2.82/3.17 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | A != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(524,a,515,a)].
% 3.04/3.32 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),D)) | C = D | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(524,a,518,a)].
% 3.04/3.32 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C) | B = C. [resolve(524,a,520,a)].
% 3.04/3.32 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(524,a,521,a)].
% 3.04/3.32 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)) | B = D | A = C. [resolve(524,a,522,a)].
% 3.04/3.32 525 class_Ring__and__Field_Oordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 3.04/3.32 526 -class_Ring__and__Field_Oordered__semiring(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A) # label(cls_mult__right__less__imp__less_0) # label(axiom). [assumption].
% 3.04/3.32 527 -class_Ring__and__Field_Oordered__semiring(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) # label(cls_mult__left__less__imp__less_0) # label(axiom). [assumption].
% 3.04/3.32 528 class_Ring__and__Field_Oordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 3.04/3.32 529 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 3.04/3.32 530 -class_Nat_Osemiring__char__0(A) | c_Nat_Osemiring__1__class_Oof__nat(B,A) != c_Nat_Osemiring__1__class_Oof__nat(C,A) | B = C # label(cls_of__nat__eq__iff_0) # label(axiom). [assumption].
% 3.04/3.32 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(529,a,530,a)].
% 3.04/3.32 531 class_Nat_Osemiring__char__0(tc_Int_Oint) # label(clsarity_Int__Oint__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 3.04/3.32 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(531,a,530,a)].
% 3.04/3.32 532 class_Nat_Osemiring__char__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 3.04/3.32 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(532,a,530,a)].
% 3.04/3.32 533 class_Ring__and__Field_Olordered__ring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Olordered__ring) # label(axiom). [assumption].
% 3.04/3.32 534 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oabs__class_Oabs(B,A)),c_HOL_Oabs__class_Oabs(C,A)),A) # label(cls_abs__le__mult_0) # label(axiom). [assumption].
% 3.04/3.32 Derived: c_lessequals(c_HOL_Oabs__class_Oabs(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oabs__class_Oabs(A,tc_Int_Oint)),c_HOL_Oabs__class_Oabs(B,tc_Int_Oint)),tc_Int_Oint). [resolve(533,a,534,a)].
% 3.04/3.32 535 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 3.04/3.32 536 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oone__class_Oone(A)) = B # label(cls_mult__1__right_0) # label(axiom). [assumption].
% 3.04/3.32 537 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_mult__1__left_0) # label(axiom). [assumption].
% 3.04/3.32 538 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) # label(cls_power__Suc2_0) # label(axiom). [assumption].
% 3.04/3.32 539 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) # label(cls_power__add_0) # label(axiom). [assumption].
% 3.04/3.32 540 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D) # label(cls_power__mult_0) # label(axiom). [assumption].
% 3.04/3.32 541 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Oone__class_Oone(tc_nat)) = B # label(cls_power__one__right_0) # label(axiom). [assumption].
% 3.04/3.32 542 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_power__commutes_0) # label(axiom). [assumption].
% 3.04/3.32 543 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Oone__class_Oone(A)),B) = c_HOL_Oone__class_Oone(A) # label(cls_power__one_0) # label(axiom). [assumption].
% 3.04/3.32 544 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Suc(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) # label(cls_power__odd__eq_0) # label(axiom). [assumption].
% 3.04/3.32 545 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B)),B) # label(cls_power3__eq__cube_0) # label(axiom). [assumption].
% 3.04/3.32 546 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) # label(cls_power__even__eq_0) # label(axiom). [assumption].
% 3.04/3.32 547 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B) # label(cls_power2__eq__square_0) # label(axiom). [assumption].
% 3.04/3.32 548 -class_OrderedGroup_Omonoid__mult(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Int_Onumber__class_Onumber__of(B,A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),c_Int_Onumber__class_Onumber__of(B,A)) # label(cls_power2__eq__square__number__of_0) # label(axiom). [assumption].
% 3.04/3.32 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),A). [resolve(535,a,538,a)].
% 3.04/3.33 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C)). [resolve(535,a,539,a)].
% 3.04/3.33 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),C). [resolve(535,a,540,a)].
% 3.04/3.33 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = c_HOL_Oone__class_Oone(tc_nat). [resolve(535,a,543,a)].
% 3.04/3.33 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Suc(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))). [resolve(535,a,544,a)].
% 3.04/3.33 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),A)),A). [resolve(535,a,545,a)].
% 3.04/3.33 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(535,a,546,a)].
% 3.04/3.33 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),A). [resolve(535,a,547,a)].
% 3.04/3.33 549 class_OrderedGroup_Omonoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 3.04/3.33 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),A). [resolve(549,a,538,a)].
% 3.04/3.33 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)). [resolve(549,a,539,a)].
% 3.04/3.33 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),C). [resolve(549,a,540,a)].
% 3.04/3.33 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),A) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(549,a,543,a)].
% 3.04/3.33 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Suc(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))). [resolve(549,a,544,a)].
% 3.04/3.33 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A)),A). [resolve(549,a,545,a)].
% 3.04/3.33 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(549,a,546,a)].
% 3.04/3.37 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A). [resolve(549,a,547,a)].
% 3.04/3.37 550 class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 3.04/3.37 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Suc(B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),A). [resolve(550,a,538,a)].
% 3.04/3.37 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),C)). [resolve(550,a,539,a)].
% 3.04/3.37 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),C). [resolve(550,a,540,a)].
% 3.04/3.37 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(550,a,543,a)].
% 3.04/3.37 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Suc(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))). [resolve(550,a,544,a)].
% 3.04/3.37 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),A)),A). [resolve(550,a,545,a)].
% 3.04/3.37 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(550,a,546,a)].
% 3.04/3.37 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),A). [resolve(550,a,547,a)].
% 3.04/3.37 551 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 3.04/3.37 552 -class_OrderedGroup_Ocomm__monoid__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_mult__1_0) # label(axiom). [assumption].
% 3.04/3.37 553 -class_OrderedGroup_Ocomm__monoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) # label(cls_power__mult__distrib_0) # label(axiom). [assumption].
% 3.04/3.37 554 class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 3.04/3.37 555 class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 3.13/3.40 556 class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) # label(axiom). [assumption].
% 3.13/3.40 557 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(B,A),A) = B # label(cls_inverse__inverse__eq_0) # label(axiom). [assumption].
% 3.13/3.40 558 -class_Ring__and__Field_Odivision__ring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) != c_HOL_Oone__class_Oone(A) | c_HOL_Oinverse__class_Oinverse(B,A) = C # label(cls_inverse__unique_0) # label(axiom). [assumption].
% 3.13/3.40 559 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Oinverse__class_Oinverse(C,A) | B = C # label(cls_inverse__eq__iff__eq_0) # label(axiom). [assumption].
% 3.13/3.40 560 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Oinverse__class_Oinverse(C,A) | B = C | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__eq__imp__eq_0) # label(axiom). [assumption].
% 3.13/3.40 561 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__nonzero__iff__nonzero_1) # label(axiom). [assumption].
% 3.13/3.40 562 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(B,A),A) # label(cls_inverse__minus__eq_0) # label(axiom). [assumption].
% 3.13/3.40 563 -class_Ring__and__Field_Odivision__ring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Oinverse(B,A)),B) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_left__inverse_0) # label(axiom). [assumption].
% 3.13/3.40 564 -class_Ring__and__Field_Odivision__ring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oinverse__class_Oinverse(B,A)) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_right__inverse_0) # label(axiom). [assumption].
% 3.13/3.40 565 -class_Ring__and__Field_Odivision__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oinverse__class_Oinverse(B,A)),c_HOL_Oinverse__class_Oinverse(C,A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Oinverse(B,A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))),c_HOL_Oinverse__class_Oinverse(C,A)) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_division__ring__inverse__add_0) # label(axiom). [assumption].
% 3.13/3.40 566 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Oinverse(C,A)),c_HOL_Oinverse__class_Oinverse(B,A)) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__mult__distrib_0) # label(axiom). [assumption].
% 3.13/3.40 567 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(B,A),A) = B | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__inverse__eq_0) # label(axiom). [assumption].
% 3.13/3.40 568 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Oinverse__class_Oinverse(B,A)),C) # label(cls_power__inverse_0) # label(axiom). [assumption].
% 3.13/3.40 569 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Oinverse__class_Oinverse(B,A)),C) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__power__inverse_0) # label(axiom). [assumption].
% 3.13/3.40 570 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(B,A),A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(B,A),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__inverse__minus__eq_0) # label(axiom). [assumption].
% 3.13/3.41 571 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(A),A) = c_HOL_Oone__class_Oone(A) # label(cls_inverse__1_0) # label(axiom). [assumption].
% 3.13/3.41 572 -class_Ring__and__Field_Odivision__ring(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__nonzero__iff__nonzero_0) # label(axiom). [assumption].
% 3.13/3.41 573 -class_Ring__and__Field_Odivision__ring(A) | c_HOL_Oinverse__class_Oinverse(B,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_inverse__zero__imp__zero_0) # label(axiom). [assumption].
% 3.13/3.41 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A. [resolve(556,a,557,a)].
% 3.13/3.41 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex) = B. [resolve(556,a,558,a)].
% 3.13/3.41 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex) | A = B. [resolve(556,a,559,a)].
% 3.13/3.41 Derived: c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex) != c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex) | A = B | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(556,a,560,a)].
% 3.13/3.41 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(556,a,561,a)].
% 3.13/3.41 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(556,a,562,a)].
% 3.13/3.41 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(556,a,564,a)].
% 3.13/3.41 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex)),c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B))),c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex)) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(556,a,565,a)].
% 3.13/3.41 Derived: c_HOL_Oinverse__class_Oinverse(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(B,tc_Complex_Ocomplex)),c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex)) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(556,a,566,a)].
% 3.13/3.41 Derived: c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = A | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(556,a,567,a)].
% 3.13/3.41 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex)),B). [resolve(556,a,568,a)].
% 3.13/3.45 Derived: c_HOL_Oinverse__class_Oinverse(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex)),B) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(556,a,569,a)].
% 3.13/3.45 Derived: c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(556,a,570,a)].
% 3.13/3.45 Derived: c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(556,a,571,a)].
% 3.13/3.45 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(556,a,572,a)].
% 3.13/3.46 Derived: c_HOL_Oinverse__class_Oinverse(A,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(556,a,573,a)].
% 3.13/3.46 574 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 3.13/3.46 575 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)) # label(cls_of__nat__add_0) # label(axiom). [assumption].
% 3.13/3.46 576 -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].
% 3.13/3.46 577 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A)) # label(cls_of__nat__Suc_0) # label(axiom). [assumption].
% 3.13/3.46 578 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_of__nat__1_0) # label(axiom). [assumption].
% 3.13/3.46 579 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)) # label(cls_of__nat__mult_0) # label(axiom). [assumption].
% 3.13/3.46 580 -class_Ring__and__Field_Osemiring__1(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Int_Oiszero(B,A) # label(cls_iszero__def_0) # label(axiom). [assumption].
% 3.13/3.46 581 -class_Ring__and__Field_Osemiring__1(A) | c_Int_Oiszero(c_HOL_Ozero__class_Ozero(A),A) # label(cls_iszero__0_0) # label(axiom). [assumption].
% 3.13/3.46 582 -class_Ring__and__Field_Osemiring__1(A) | -c_Int_Oiszero(c_HOL_Oone__class_Oone(A),A) # label(cls_not__iszero__1_0) # label(axiom). [assumption].
% 3.13/3.46 583 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),C),A) = hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),C) # label(cls_of__nat__power_0) # label(axiom). [assumption].
% 3.13/3.46 584 -class_Ring__and__Field_Osemiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = c_HOL_Ozero__class_Ozero(A) # label(cls_zero__power2_0) # label(axiom). [assumption].
% 3.13/3.46 585 -class_Ring__and__Field_Osemiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Oone__class_Oone(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = c_HOL_Oone__class_Oone(A) # label(cls_one__power2_0) # label(axiom). [assumption].
% 3.13/3.46 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat)). [resolve(574,a,575,a)].
% 3.13/3.46 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(574,a,576,a)].
% 3.13/3.46 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)). [resolve(574,a,577,a)].
% 3.13/3.46 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(574,a,578,a)].
% 3.13/3.46 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat)). [resolve(574,a,579,a)].
% 3.13/3.46 Derived: A = c_HOL_Ozero__class_Ozero(tc_nat) | -c_Int_Oiszero(A,tc_nat). [resolve(574,a,580,a)].
% 3.13/3.46 Derived: c_Int_Oiszero(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(574,a,581,a)].
% 3.13/3.46 Derived: -c_Int_Oiszero(c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(574,a,582,a)].
% 3.13/3.46 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),B). [resolve(574,a,583,a)].
% 3.13/3.46 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(574,a,584,a)].
% 3.13/3.46 586 class_Ring__and__Field_Osemiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 3.13/3.46 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint)). [resolve(586,a,575,a)].
% 3.13/3.46 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(586,a,576,a)].
% 3.13/3.46 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint)). [resolve(586,a,577,a)].
% 3.13/3.46 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(586,a,578,a)].
% 3.13/3.46 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_Int_Oint) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint)). [resolve(586,a,579,a)].
% 3.13/3.46 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Int_Oiszero(A,tc_Int_Oint). [resolve(586,a,580,a)].
% 3.13/3.46 Derived: c_Int_Oiszero(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(586,a,581,a)].
% 3.13/3.46 Derived: -c_Int_Oiszero(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(586,a,582,a)].
% 3.13/3.46 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_Int_Oint) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint)),B). [resolve(586,a,583,a)].
% 3.13/3.46 587 class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 3.13/3.46 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex)). [resolve(587,a,575,a)].
% 3.13/3.46 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(587,a,576,a)].
% 3.22/3.50 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex)). [resolve(587,a,577,a)].
% 3.22/3.50 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(587,a,578,a)].
% 3.22/3.50 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_Complex_Ocomplex)). [resolve(587,a,579,a)].
% 3.22/3.50 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | -c_Int_Oiszero(A,tc_Complex_Ocomplex). [resolve(587,a,580,a)].
% 3.22/3.50 Derived: c_Int_Oiszero(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(587,a,581,a)].
% 3.22/3.50 Derived: -c_Int_Oiszero(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(587,a,582,a)].
% 3.22/3.50 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Nat_Osemiring__1__class_Oof__nat(A,tc_Complex_Ocomplex)),B). [resolve(587,a,583,a)].
% 3.22/3.50 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(587,a,584,a)].
% 3.22/3.50 588 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 3.22/3.50 589 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__nonneg__nonneg_0) # label(axiom). [assumption].
% 3.22/3.50 590 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_split__mult__neg__le_0) # label(axiom). [assumption].
% 3.22/3.50 591 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_split__mult__neg__le_1) # label(axiom). [assumption].
% 3.22/3.50 592 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__nonneg__nonpos_0) # label(axiom). [assumption].
% 3.22/3.50 593 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_mult__nonpos__nonneg_0) # label(axiom). [assumption].
% 3.22/3.50 594 -class_Ring__and__Field_Opordered__cancel__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_mult__nonneg__nonpos2_0) # label(axiom). [assumption].
% 3.22/3.50 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(588,a,589,a)].
% 3.22/3.50 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). [resolve(588,a,590,a)].
% 3.22/3.57 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(588,a,591,a)].
% 3.22/3.57 595 class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 3.22/3.57 596 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 3.22/3.57 597 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) # label(axiom). [assumption].
% 3.22/3.57 598 class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 3.22/3.57 599 class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 3.22/3.57 600 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 3.22/3.57 601 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_mult__right_Oadd_0) # label(axiom). [assumption].
% 3.22/3.57 602 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_mult_Oadd__right_0) # label(axiom). [assumption].
% 3.22/3.57 603 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_mult__left_Oadd_0) # label(axiom). [assumption].
% 3.22/3.57 604 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_mult_Oadd__left_0) # label(axiom). [assumption].
% 3.22/3.57 605 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ouminus__class_Ouminus(B,A)),C) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_mult_Ominus__left_0) # label(axiom). [assumption].
% 3.22/3.57 606 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ouminus__class_Ouminus(B,A)),C) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_mult__left_Ominus_0) # label(axiom). [assumption].
% 3.22/3.57 607 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ouminus__class_Ouminus(C,A)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_mult_Ominus__right_0) # label(axiom). [assumption].
% 3.22/3.57 608 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ouminus__class_Ouminus(C,A)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A) # label(cls_mult__right_Ominus_0) # label(axiom). [assumption].
% 3.22/3.57 609 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__left_Ozero_0) # label(axiom). [assumption].
% 3.34/3.68 610 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__left_0) # label(axiom). [assumption].
% 3.34/3.68 611 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult_Ozero__right_0) # label(axiom). [assumption].
% 3.34/3.68 612 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__right_Ozero_0) # label(axiom). [assumption].
% 3.34/3.68 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),B) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex). [resolve(600,a,605,a)].
% 3.34/3.68 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex)) = c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex). [resolve(600,a,607,a)].
% 3.34/3.68 613 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 3.34/3.68 614 -class_Ring__and__Field_Ocomm__semiring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_comm__semiring__class_Odistrib_0) # label(axiom). [assumption].
% 3.34/3.68 615 class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 3.34/3.68 616 class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 3.34/3.68 617 class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add) # label(axiom). [assumption].
% 3.34/3.68 618 -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].
% 3.34/3.68 619 -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].
% 3.34/3.68 620 -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].
% 3.34/3.68 621 -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].
% 3.34/3.68 622 -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].
% 3.34/3.68 623 -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].
% 3.34/3.68 Derived: c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint) != A | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(617,a,618,a)].
% 3.34/3.68 624 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 3.34/3.68 625 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__mono_0) # label(axiom). [assumption].
% 3.45/3.72 626 -class_Ring__and__Field_Opordered__semiring(A) | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(C,E,A) | -c_lessequals(B,D,A) # label(cls_mult__mono_H_0) # label(axiom). [assumption].
% 3.45/3.72 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(624,a,625,a)].
% 3.45/3.72 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) | -c_lessequals(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(624,a,626,a)].
% 3.45/3.72 627 class_Ring__and__Field_Opordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 3.45/3.72 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D),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(627,a,625,a)].
% 3.45/3.72 Derived: c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D),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(627,a,626,a)].
% 3.45/3.72 628 class_OrderedGroup_Oab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 3.45/3.72 629 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_add__cancel__21_1) # label(axiom). [assumption].
% 3.45/3.72 630 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ouminus__class_Ouminus(B,A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_ab__left__minus_0) # label(axiom). [assumption].
% 3.45/3.72 631 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) != C | B = c_HOL_Ouminus__class_Ouminus(D,A) # label(cls_add__cancel__end_0) # label(axiom). [assumption].
% 3.45/3.72 632 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) = E # label(cls_add__cancel__21_0) # label(axiom). [assumption].
% 3.45/3.72 633 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ouminus__class_Ouminus(B,A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B)) = C # label(cls_add__cancel__end_1) # label(axiom). [assumption].
% 3.45/3.72 634 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ouminus__class_Ouminus(B,A)),c_HOL_Ouminus__class_Ouminus(C,A)) # label(cls_minus__add__distrib_0) # label(axiom). [assumption].
% 3.45/3.72 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)) != B | A = c_HOL_Ouminus__class_Ouminus(C,tc_Int_Oint). [resolve(628,a,631,a)].
% 3.45/3.72 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),D) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C) = D. [resolve(628,a,632,a)].
% 3.45/3.79 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),A)) = B. [resolve(628,a,633,a)].
% 3.45/3.79 Derived: c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint)),c_HOL_Ouminus__class_Ouminus(B,tc_Int_Oint)). [resolve(628,a,634,a)].
% 3.45/3.79 635 class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 3.45/3.79 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) != B | A = c_HOL_Ouminus__class_Ouminus(C,tc_Complex_Ocomplex). [resolve(635,a,631,a)].
% 3.45/3.79 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),C)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),D) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C) = D. [resolve(635,a,632,a)].
% 3.45/3.79 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),A)) = B. [resolve(635,a,633,a)].
% 3.45/3.79 Derived: c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),c_HOL_Ouminus__class_Ouminus(B,tc_Complex_Ocomplex)). [resolve(635,a,634,a)].
% 3.45/3.79 636 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 3.45/3.79 637 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 3.45/3.79 638 class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 3.45/3.79 639 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 3.45/3.79 640 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 3.45/3.79 641 -class_Ring__and__Field_Osemiring(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D)) # label(cls_right__distrib__number__of_0) # label(axiom). [assumption].
% 3.45/3.79 642 -class_Ring__and__Field_Osemiring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C)),E) # label(cls_combine__common__factor_0) # label(axiom). [assumption].
% 3.45/3.79 643 -class_Ring__and__Field_Osemiring(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),c_Int_Onumber__class_Onumber__of(D,A)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(D,A))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),c_Int_Onumber__class_Onumber__of(D,A))) # label(cls_left__distrib__number__of_0) # label(axiom). [assumption].
% 3.45/3.79 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B)),D). [resolve(640,a,642,a)].
% 3.55/3.90 644 class_Ring__and__Field_Osemiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 3.55/3.90 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C)),B)),D). [resolve(644,a,642,a)].
% 3.55/3.90 645 class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 3.55/3.90 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C)),B)),D). [resolve(645,a,642,a)].
% 3.55/3.90 646 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 3.55/3.90 647 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(B,A),C,A) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(B,C,A),A) # label(cls_divide_Ominus_0) # label(axiom). [assumption].
% 3.55/3.90 648 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide_Ozero_0) # label(axiom). [assumption].
% 3.55/3.90 649 -class_RealVector_Oreal__normed__field(A) | c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oinverse__class_Odivide(B,D,A)),c_HOL_Oinverse__class_Odivide(C,D,A)) # label(cls_divide_Oadd_0) # label(axiom). [assumption].
% 3.55/3.90 Derived: c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(A,B,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(646,a,647,a)].
% 3.55/3.90 650 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.55/3.90 651 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__imp__eq_0) # label(axiom). [assumption].
% 3.55/3.90 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C) | B = C. [resolve(650,a,651,a)].
% 3.55/3.90 652 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.55/3.90 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C) | B = C. [resolve(652,a,651,a)].
% 3.55/3.90 653 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.55/3.90 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),C) | B = C. [resolve(653,a,651,a)].
% 3.55/3.90 654 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 3.55/3.90 655 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__left__cancel_0) # label(axiom). [assumption].
% 3.72/4.00 656 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C) | B = D # label(cls_add__right__cancel_0) # label(axiom). [assumption].
% 3.72/4.00 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B) | A = C. [resolve(654,a,656,a)].
% 3.72/4.00 657 class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 3.72/4.00 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),B) | A = C. [resolve(657,a,656,a)].
% 3.72/4.00 658 class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 3.72/4.00 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),B) | A = C. [resolve(658,a,656,a)].
% 3.72/4.00 659 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 3.72/4.00 660 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_mult__strict__left__mono__comm_0) # label(axiom). [assumption].
% 3.72/4.00 661 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 3.72/4.00 662 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 3.72/4.00 663 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_monoid__add__class_Oadd__0__right_0) # label(axiom). [assumption].
% 3.72/4.00 664 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_add__0__left_0) # label(axiom). [assumption].
% 3.72/4.00 665 class_OrderedGroup_Omonoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 3.72/4.00 666 class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 3.72/4.00 667 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.72/4.00 668 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_lessequals(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 3.72/4.00 669 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_lessequals(B,D,A) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 3.72/4.00 670 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 3.72/4.00 671 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 3.72/4.00 672 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) | -c_HOL_Oord__class_Oless(C,E,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 3.72/4.07 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_lessequals(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(667,a,668,a)].
% 3.72/4.07 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(667,a,669,a)].
% 3.72/4.07 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat) | -c_HOL_Oord__class_Oless(B,D,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(667,a,672,a)].
% 3.72/4.07 673 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.72/4.07 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),D),tc_Int_Oint) | -c_lessequals(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(673,a,668,a)].
% 3.72/4.07 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),D),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(673,a,669,a)].
% 3.72/4.07 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),D),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,C,tc_Int_Oint). [resolve(673,a,672,a)].
% 3.72/4.07 674 class_Ring__and__Field_Oring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 3.72/4.07 675 -class_Ring__and__Field_Oring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ouminus__class_Ouminus(B,A)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(A),A)),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_power__minus_0) # label(axiom). [assumption].
% 3.72/4.07 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint)),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)). [resolve(674,a,675,a)].
% 3.72/4.07 676 class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 3.72/4.07 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)). [resolve(676,a,675,a)].
% 3.72/4.07 677 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].
% 3.72/4.07 678 -class_Ring__and__Field_Oring__1__no__zero__divisors(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_field__power__not__zero_0) # label(axiom). [assumption].
% 3.72/4.07 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(677,a,678,a)].
% 3.72/4.07 679 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].
% 3.72/4.07 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(679,a,678,a)].
% 3.85/4.11 680 class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1) # label(axiom). [assumption].
% 3.85/4.11 681 -class_Ring__and__Field_Ocomm__ring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(A),A)),c_Suc(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B))) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(A),A) # label(cls_power__minus1__odd_0) # label(axiom). [assumption].
% 3.85/4.11 682 -class_Ring__and__Field_Ocomm__ring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(A),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)) = c_HOL_Oone__class_Oone(A) # label(cls_power__minus1__even_0) # label(axiom). [assumption].
% 3.85/4.11 683 -class_Ring__and__Field_Ocomm__ring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ouminus__class_Ouminus(B,A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C)) # label(cls_comm__ring__1__class_Opower__minus__even_0) # label(axiom). [assumption].
% 3.85/4.11 684 -class_Ring__and__Field_Ocomm__ring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ouminus__class_Ouminus(B,A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) # label(cls_power2__minus_0) # label(axiom). [assumption].
% 3.85/4.11 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint)),c_Suc(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A))) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(680,a,681,a)].
% 3.85/4.11 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A)) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(680,a,682,a)].
% 3.85/4.11 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)). [resolve(680,a,683,a)].
% 3.85/4.11 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ouminus__class_Ouminus(A,tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(680,a,684,a)].
% 3.85/4.11 685 class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) # label(axiom). [assumption].
% 3.85/4.11 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)),c_Suc(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A))) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(685,a,681,a)].
% 3.85/4.11 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(685,a,682,a)].
% 3.86/4.14 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)). [resolve(685,a,683,a)].
% 3.86/4.14 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(A,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(685,a,684,a)].
% 3.86/4.14 686 class_Int_Oring__char__0(tc_Int_Oint) # label(clsarity_Int__Oint__Int_Oring__char__0) # label(axiom). [assumption].
% 3.86/4.14 687 -class_Int_Oring__char__0(A) | -class_Int_Onumber__ring(A) | -c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(B),A),A) # label(cls_iszero__number__of__Bit1_0) # label(axiom). [assumption].
% 3.86/4.14 688 -class_Int_Oring__char__0(A) | -class_Int_Onumber__ring(A) | c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(B,A),A) | -c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(B),A),A) # label(cls_iszero__number__of__Bit0_0) # label(axiom). [assumption].
% 3.86/4.14 689 -class_Int_Oring__char__0(A) | -class_Int_Onumber__ring(A) | c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(B),A),A) | -c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_iszero__number__of__Bit0_1) # label(axiom). [assumption].
% 3.86/4.14 690 -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].
% 3.86/4.14 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(A),tc_Int_Oint),tc_Int_Oint). [resolve(686,a,687,a)].
% 3.86/4.14 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint) | -c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(A),tc_Int_Oint),tc_Int_Oint). [resolve(686,a,688,a)].
% 3.86/4.14 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(A),tc_Int_Oint),tc_Int_Oint) | -c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint). [resolve(686,a,689,a)].
% 3.86/4.14 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint) | A = B. [resolve(686,a,690,a)].
% 3.86/4.14 691 class_Int_Oring__char__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Int_Oring__char__0) # label(axiom). [assumption].
% 3.86/4.14 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | -c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(A),tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(691,a,687,a)].
% 3.86/4.14 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(A),tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(691,a,688,a)].
% 3.86/4.14 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(A),tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(691,a,689,a)].
% 3.86/4.14 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_Int_Onumber__class_OnumCputime limit exceeded (core dumped)
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