TSTP Solution File: SWV655-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV655-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.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 21:14:18 EDT 2022
% Result : Timeout 300.07s 300.29s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV655-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 15 19:15:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.44/1.69 ============================== Prover9 ===============================
% 1.44/1.69 Prover9 (32) version 2009-11A, November 2009.
% 1.44/1.69 Process 22082 was started by sandbox2 on n016.cluster.edu,
% 1.44/1.69 Wed Jun 15 19:15:19 2022
% 1.44/1.69 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_21928_n016.cluster.edu".
% 1.44/1.69 ============================== end of head ===========================
% 1.44/1.69
% 1.44/1.69 ============================== INPUT =================================
% 1.44/1.69
% 1.44/1.69 % Reading from file /tmp/Prover9_21928_n016.cluster.edu
% 1.44/1.69
% 1.44/1.69 set(prolog_style_variables).
% 1.44/1.69 set(auto2).
% 1.44/1.69 % set(auto2) -> set(auto).
% 1.44/1.69 % set(auto) -> set(auto_inference).
% 1.44/1.69 % set(auto) -> set(auto_setup).
% 1.44/1.69 % set(auto_setup) -> set(predicate_elim).
% 1.44/1.69 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.44/1.69 % set(auto) -> set(auto_limits).
% 1.44/1.69 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.44/1.69 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.44/1.69 % set(auto) -> set(auto_denials).
% 1.44/1.69 % set(auto) -> set(auto_process).
% 1.44/1.69 % set(auto2) -> assign(new_constants, 1).
% 1.44/1.69 % set(auto2) -> assign(fold_denial_max, 3).
% 1.44/1.69 % set(auto2) -> assign(max_weight, "200.000").
% 1.44/1.69 % set(auto2) -> assign(max_hours, 1).
% 1.44/1.69 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.44/1.69 % set(auto2) -> assign(max_seconds, 0).
% 1.44/1.69 % set(auto2) -> assign(max_minutes, 5).
% 1.44/1.69 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.44/1.69 % set(auto2) -> set(sort_initial_sos).
% 1.44/1.69 % set(auto2) -> assign(sos_limit, -1).
% 1.44/1.69 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.44/1.69 % set(auto2) -> assign(max_megs, 400).
% 1.44/1.69 % set(auto2) -> assign(stats, some).
% 1.44/1.69 % set(auto2) -> clear(echo_input).
% 1.44/1.69 % set(auto2) -> set(quiet).
% 1.44/1.69 % set(auto2) -> clear(print_initial_clauses).
% 1.44/1.69 % set(auto2) -> clear(print_given).
% 1.44/1.69 assign(lrs_ticks,-1).
% 1.44/1.69 assign(sos_limit,10000).
% 1.44/1.69 assign(order,kbo).
% 1.44/1.69 set(lex_order_vars).
% 1.44/1.69 clear(print_given).
% 1.44/1.69
% 1.44/1.69 % formulas(sos). % not echoed (1373 formulas)
% 1.44/1.69
% 1.44/1.69 ============================== end of input ==========================
% 1.44/1.69
% 1.44/1.69 % From the command line: assign(max_seconds, 300).
% 1.44/1.69
% 1.44/1.69 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.44/1.69
% 1.44/1.69 % Formulas that are not ordinary clauses:
% 1.44/1.69
% 1.44/1.69 ============================== end of process non-clausal formulas ===
% 1.44/1.69
% 1.44/1.69 ============================== PROCESS INITIAL CLAUSES ===============
% 1.44/1.69
% 1.44/1.69 ============================== PREDICATE ELIMINATION =================
% 1.44/1.69 1 class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) # label(axiom). [assumption].
% 1.44/1.69 2 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),C),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].
% 1.44/1.69 3 -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,hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) # label(cls_le__eq__neg_0) # label(axiom). [assumption].
% 1.44/1.69 4 -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].
% 1.44/1.69 5 -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].
% 1.44/1.69 6 -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].
% 1.44/1.69 7 -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].
% 1.44/1.69 8 -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].
% 1.44/1.69 9 -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].
% 1.44/1.69 10 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_le__minus__self__iff_0) # label(axiom). [assumption].
% 1.44/1.69 11 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_le__minus__self__iff_1) # label(axiom). [assumption].
% 1.44/1.69 12 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),B,A) # label(cls_minus__le__self__iff_0) # label(axiom). [assumption].
% 1.44/1.69 13 -class_OrderedGroup_Olordered__ab__group__add(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_minus__le__self__iff_1) # label(axiom). [assumption].
% 1.44/1.69 14 -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].
% 1.44/1.69 15 -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].
% 1.44/1.69 16 -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].
% 1.44/1.69 17 -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].
% 1.44/1.69 Derived: c_lessequals(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B),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(1,a,2,a)].
% 1.44/1.69 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,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B),tc_Int_Oint). [resolve(1,a,3,a)].
% 1.44/1.69 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(1,a,4,a)].
% 1.44/1.69 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(1,a,5,a)].
% 1.44/1.69 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(1,a,6,a)].
% 1.44/1.69 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(1,a,7,a)].
% 1.44/1.73 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(1,a,8,a)].
% 1.44/1.73 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(1,a,9,a)].
% 1.44/1.73 Derived: c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint). [resolve(1,a,10,a)].
% 1.44/1.73 Derived: c_lessequals(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(1,a,11,a)].
% 1.44/1.73 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),A,tc_Int_Oint). [resolve(1,a,12,a)].
% 1.44/1.73 Derived: c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),A,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(1,a,13,a)].
% 1.44/1.73 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(1,a,14,a)].
% 1.44/1.73 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(1,a,15,a)].
% 1.44/1.73 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(1,a,16,a)].
% 1.44/1.73 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(1,a,17,a)].
% 1.44/1.73 18 -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].
% 1.44/1.73 19 hAPP(hAPP(A,B),hAPP(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].
% 1.44/1.73 20 hAPP(hAPP(A,B),hAPP(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].
% 1.44/1.73 21 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),C) = hAPP(hAPP(B,C),hAPP(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].
% 1.44/1.73 22 hAPP(hAPP(A,B),hAPP(hAPP(C,B),D)) = hAPP(hAPP(C,B),hAPP(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].
% 1.44/1.73 23 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].
% 1.44/1.73 24 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].
% 1.44/1.73 25 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].
% 1.44/1.73 26 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].
% 1.44/1.73 27 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].
% 1.44/1.73 28 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].
% 1.44/1.73 29 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].
% 1.44/1.73 30 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].
% 1.44/1.73 31 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].
% 1.44/1.73 32 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].
% 1.44/1.73 33 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].
% 1.44/1.73 34 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].
% 1.44/1.73 35 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].
% 1.44/1.73 36 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].
% 1.44/1.73 37 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].
% 1.44/1.73 38 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].
% 1.44/1.73 39 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].
% 1.44/1.73 40 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].
% 1.44/1.73 41 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].
% 1.44/1.73 42 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].
% 1.44/1.73 43 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].
% 1.44/1.73 44 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].
% 1.44/1.73 45 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].
% 1.44/1.73 46 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].
% 1.44/1.73 47 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].
% 1.44/1.73 48 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].
% 1.44/1.73 49 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].
% 1.61/1.86 50 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].
% 1.61/1.86 51 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].
% 1.61/1.86 52 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].
% 1.61/1.86 53 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].
% 1.61/1.86 54 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].
% 1.61/1.86 55 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].
% 1.61/1.86 56 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].
% 1.61/1.86 57 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].
% 1.61/1.86 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B. [resolve(18,b,28,b)].
% 1.61/1.86 Derived: -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B. [resolve(18,b,29,b)].
% 1.61/1.86 Derived: -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). [resolve(18,b,32,b)].
% 1.61/1.86 Derived: -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). [resolve(18,b,33,b)].
% 1.61/1.86 58 hAPP(hAPP(A,B),hAPP(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].
% 1.61/1.86 59 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].
% 1.61/1.86 60 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].
% 1.61/1.86 61 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].
% 1.61/1.86 62 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].
% 1.61/1.86 63 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].
% 1.61/1.86 64 class_Ring__and__Field_Opordered__ring__abs(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs) # label(axiom). [assumption].
% 1.61/1.86 65 -class_Ring__and__Field_Opordered__ring__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__eq__mult_3) # label(axiom). [assumption].
% 1.69/1.93 66 -class_Ring__and__Field_Opordered__ring__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C)) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__eq__mult_2) # label(axiom). [assumption].
% 1.69/1.93 67 -class_Ring__and__Field_Opordered__ring__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C)) | -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__eq__mult_1) # label(axiom). [assumption].
% 1.69/1.93 68 -class_Ring__and__Field_Opordered__ring__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C)) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__eq__mult_0) # label(axiom). [assumption].
% 1.69/1.93 Derived: hAPP(c_HOL_Oabs__class_Oabs(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),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)) | -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(64,a,65,a)].
% 1.69/1.93 Derived: hAPP(c_HOL_Oabs__class_Oabs(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),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)) | -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(64,a,66,a)].
% 1.69/1.93 Derived: hAPP(c_HOL_Oabs__class_Oabs(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),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)) | -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(64,a,67,a)].
% 1.69/1.93 Derived: hAPP(c_HOL_Oabs__class_Oabs(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),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),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(64,a,68,a)].
% 1.69/1.93 69 class_Ring__and__Field_Oordered__idom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__idom) # label(axiom). [assumption].
% 1.69/1.93 70 -class_Ring__and__Field_Oordered__idom(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(hAPP(c_HOL_Oabs__class_Oabs(A),B),hAPP(c_HOL_Oabs__class_Oabs(A),D),A) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_power__mono__even_0) # label(axiom). [assumption].
% 1.69/1.93 71 -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].
% 1.69/1.93 72 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),B),C,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_abs__less__iff_2) # label(axiom). [assumption].
% 1.69/1.93 73 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) | C = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__le__zero__eq_4) # label(axiom). [assumption].
% 1.69/1.93 74 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_power__less__zero__eq_2) # label(axiom). [assumption].
% 1.69/1.93 75 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq_1) # label(axiom). [assumption].
% 1.69/1.93 76 -class_Ring__and__Field_Oordered__idom(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(B,D,A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_power__mono__odd_0) # label(axiom). [assumption].
% 1.69/1.93 77 -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].
% 1.69/1.93 78 -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(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__less__zero__eq__number__of_0) # label(axiom). [assumption].
% 1.69/1.93 79 -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_Parity_Oeven__odd__class_Oeven(B,tc_nat) # label(cls_zero__less__power__eq_1) # label(axiom). [assumption].
% 1.69/1.93 80 -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].
% 1.69/1.93 81 -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),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__less__power__eq_5) # label(axiom). [assumption].
% 1.69/1.93 82 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),B),C,A) # label(cls_abs__less__iff_1) # label(axiom). [assumption].
% 1.69/1.93 83 -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].
% 1.69/1.93 84 -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].
% 1.69/1.93 85 -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,tc_nat)),A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_zero__le__power__eq__number__of_2) # label(axiom). [assumption].
% 1.69/1.93 86 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A) # label(cls_zero__le__power__eq__number__of_0) # label(axiom). [assumption].
% 1.69/1.93 87 -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].
% 1.69/1.93 88 -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].
% 1.69/1.93 89 -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__less__zero__eq_0) # label(axiom). [assumption].
% 1.69/1.93 90 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) | C = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) # label(cls_zero__less__power__eq_0) # label(axiom). [assumption].
% 1.69/1.93 91 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hAPP(c_HOL_Oabs__class_Oabs(A),c_Int_Onumber__class_Onumber__of(B,A)) = hAPP(c_HOL_Ouminus__class_Ouminus(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_0) # label(axiom). [assumption].
% 1.69/1.93 92 -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].
% 1.69/1.93 93 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E),A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),C),E,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),B),D,A) # label(cls_abs__mult__less_0) # label(axiom). [assumption].
% 1.69/1.93 94 -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].
% 1.69/1.93 95 -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,tc_nat)),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_power__less__zero__eq__number__of_2) # label(axiom). [assumption].
% 1.69/1.93 96 -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].
% 1.69/1.93 97 -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].
% 1.69/1.93 98 -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),A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__less__power__eq_4) # label(axiom). [assumption].
% 1.69/1.93 99 -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,tc_nat)),A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_zero__le__power__eq__number__of_1) # label(axiom). [assumption].
% 1.69/1.93 100 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),C),A) # label(cls_zero__le__power__abs_0) # label(axiom). [assumption].
% 1.69/1.93 101 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) | -c_lessequals(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_1) # label(axiom). [assumption].
% 1.69/1.93 102 -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].
% 1.69/1.93 103 -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat) | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq_5) # label(axiom). [assumption].
% 1.69/1.93 104 -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].
% 1.69/1.93 105 -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].
% 1.69/1.93 106 -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_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__power__eq_1) # label(axiom). [assumption].
% 1.69/1.93 107 -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_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__power__iff_2) # label(axiom). [assumption].
% 1.69/1.93 108 -class_Ring__and__Field_Oordered__idom(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) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) | c_Int_Onumber__class_Onumber__of(C,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__le__zero__eq__number__of_4) # label(axiom). [assumption].
% 1.69/1.93 109 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_power__even__abs_0) # label(axiom). [assumption].
% 1.69/1.93 110 -class_Ring__and__Field_Oordered__idom(A) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(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_2) # label(axiom). [assumption].
% 1.69/1.93 111 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),D,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),B)),C,A) # label(cls_abs__diff__less__iff_0) # label(axiom). [assumption].
% 1.69/1.93 112 -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | c_lessequals(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),A) # label(cls_power__le__zero__eq__number__of_5) # label(axiom). [assumption].
% 1.69/1.93 113 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D,A) | -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D),B,A) # label(cls_abs__diff__less__iff_2) # label(axiom). [assumption].
% 1.69/1.93 114 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),B),C,A) # label(cls_abs__less__iff_0) # label(axiom). [assumption].
% 1.69/1.93 115 -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].
% 1.69/1.93 116 -class_Ring__and__Field_Oordered__idom(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C)) = hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_abs__power__minus_0) # label(axiom). [assumption].
% 1.69/1.93 117 -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].
% 1.69/1.93 118 -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].
% 1.69/1.93 119 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),C) = hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) # label(cls_abs__mult__pos_0) # label(axiom). [assumption].
% 1.69/1.93 120 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hAPP(c_HOL_Oabs__class_Oabs(A),c_Int_Onumber__class_Onumber__of(B,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].
% 1.69/1.93 121 -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].
% 1.69/1.93 122 -class_Ring__and__Field_Oordered__idom(A) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_power__le__zero__eq_2) # label(axiom). [assumption].
% 1.69/1.93 123 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) | c_Int_Onumber__class_Onumber__of(C,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A) # label(cls_zero__less__power__eq__number__of_0) # label(axiom). [assumption].
% 1.69/1.93 124 -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,tc_nat)),A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_zero__less__power__eq__number__of_5) # label(axiom). [assumption].
% 1.69/1.93 125 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B) # label(cls_abs__mult__self_0) # label(axiom). [assumption].
% 1.69/1.93 126 -class_Ring__and__Field_Oordered__idom(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C)) # label(cls_abs__mult_0) # label(axiom). [assumption].
% 1.69/1.93 127 -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].
% 1.69/1.93 128 -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].
% 1.69/1.93 129 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hAPP(c_HOL_Oabs__class_Oabs(A),c_Int_Onumber__class_Onumber__of(c_Int_OMin,A)) = c_HOL_Oone__class_Oone(A) # label(cls_abs__minus__one_0) # label(axiom). [assumption].
% 1.69/1.93 130 -class_Ring__and__Field_Oordered__idom(A) | hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Oone__class_Oone(A)) = c_HOL_Oone__class_Oone(A) # label(cls_abs__one_0) # label(axiom). [assumption].
% 1.69/1.93 131 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D,A) # label(cls_abs__diff__less__iff_1) # label(axiom). [assumption].
% 1.69/1.93 132 -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,tc_nat)),A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_zero__less__power__eq__number__of_4) # label(axiom). [assumption].
% 1.69/1.93 133 -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_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) # label(cls_zero__less__power__eq__number__of_1) # label(axiom). [assumption].
% 1.69/1.93 134 -class_Ring__and__Field_Oordered__idom(A) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B),A) # label(cls_zero__le__power__iff_0) # label(axiom). [assumption].
% 1.69/1.93 135 -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) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__odd__power_1) # label(axiom). [assumption].
% 1.69/1.93 136 -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),A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__odd__power_0) # label(axiom). [assumption].
% 1.69/1.93 137 -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) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__power__eq_2) # label(axiom). [assumption].
% 1.69/1.93 138 -class_Ring__and__Field_Oordered__idom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) # label(cls_zero__le__power__eq_0) # label(axiom). [assumption].
% 1.69/1.93 139 -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,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_less__minus__self__iff_0) # label(axiom). [assumption].
% 1.69/1.93 140 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_less__minus__self__iff_1) # label(axiom). [assumption].
% 1.69/1.93 141 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Int_Onumber__class_Onumber__of(c_Int_OMin,A)),B)) = c_HOL_Oone__class_Oone(A) # label(cls_abs__power__minus__one_0) # label(axiom). [assumption].
% 1.69/1.93 142 -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].
% 1.69/1.93 143 -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].
% 1.69/1.93 144 -class_Ring__and__Field_Oordered__idom(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),C) # label(cls_power__abs_0) # label(axiom). [assumption].
% 1.69/1.93 145 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),c_Int_Onumber__class_Onumber__of(C,tc_nat)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_power__even__abs__number__of_0) # label(axiom). [assumption].
% 1.69/1.93 146 -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].
% 1.69/1.93 147 -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].
% 1.69/1.93 148 -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].
% 1.69/1.93 149 -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),hAPP(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].
% 1.69/1.93 150 -class_Ring__and__Field_Oordered__idom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(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].
% 1.69/1.93 151 -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].
% 1.69/1.93 152 -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].
% 1.69/1.93 153 -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].
% 1.69/1.93 154 -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].
% 1.69/1.93 155 -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].
% 1.69/1.93 156 -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].
% 1.69/1.93 157 -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].
% 1.69/1.93 158 -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].
% 1.69/1.93 159 -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].
% 1.69/1.93 160 -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].
% 1.69/1.93 161 -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].
% 1.69/1.93 162 -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].
% 1.69/1.93 163 -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].
% 1.69/1.93 164 -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].
% 1.69/1.93 165 -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].
% 1.69/1.93 166 -class_Ring__and__Field_Oordered__idom(A) | hAPP(c_HOL_Oabs__class_Oabs(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),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].
% 1.69/1.93 167 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Oabs__class_Oabs(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),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].
% 1.69/1.93 168 -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].
% 1.69/1.93 169 -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].
% 1.69/1.93 170 -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].
% 1.69/1.93 171 -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].
% 1.69/1.93 172 -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].
% 1.69/1.93 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(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),C),tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(69,a,70,a)].
% 1.69/1.93 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(B,A,tc_Int_Oint) | B = A. [resolve(69,a,71,a)].
% 1.69/1.93 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(69,a,72,a)].
% 1.69/1.93 Derived: 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) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(69,a,73,a)].
% 1.69/1.93 Derived: 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) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(69,a,74,a)].
% 1.69/1.93 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | -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(69,a,75,a)].
% 1.69/1.93 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(A,C,tc_Int_Oint) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(69,a,76,a)].
% 1.69/1.93 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(69,a,77,a)].
% 1.69/1.93 Derived: -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(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(69,a,78,a)].
% 1.69/1.93 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_Parity_Oeven__odd__class_Oeven(A,tc_nat). [resolve(69,a,79,a)].
% 1.69/1.93 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(69,a,80,a)].
% 1.69/1.93 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) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(69,a,81,a)].
% 1.69/1.93 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),B,tc_Int_Oint). [resolve(69,a,82,a)].
% 1.69/1.93 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(B,tc_nat)),tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat). [resolve(69,a,85,a)].
% 1.69/1.93 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(B,tc_nat)),tc_Int_Oint). [resolve(69,a,86,a)].
% 1.69/1.93 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(69,a,87,a)].
% 1.69/1.93 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(69,a,88,a)].
% 1.69/1.93 Derived: -c_Parity_Oeven__odd__class_Oeven(A,tc_nat) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(69,a,89,a)].
% 1.69/1.93 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint). [resolve(69,a,90,a)].
% 1.69/1.93 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)) = hAPP(c_HOL_Ouminus__class_Ouminus(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(69,a,91,a)].
% 1.69/1.93 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(69,a,92,a)].
% 1.69/1.93 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D),tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B),D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),C,tc_Int_Oint). [resolve(69,a,93,a)].
% 1.69/1.93 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(69,a,94,a)].
% 1.69/1.93 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(69,a,96,a)].
% 1.69/1.93 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(69,a,97,a)].
% 1.69/1.93 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) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(69,a,98,a)].
% 1.69/1.93 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(B,tc_nat)),tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat). [resolve(69,a,99,a)].
% 1.69/1.93 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),B),tc_Int_Oint). [resolve(69,a,100,a)].
% 1.69/1.93 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(69,a,102,a)].
% 1.69/1.93 Derived: -c_Parity_Oeven__odd__class_Oeven(A,tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat) | c_lessequals(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),tc_Int_Oint). [resolve(69,a,103,a)].
% 1.69/1.93 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(69,a,104,a)].
% 1.69/1.93 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(69,a,105,a)].
% 1.69/1.93 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_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(69,a,106,a)].
% 1.69/1.93 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),B) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(69,a,109,a)].
% 1.69/1.93 Derived: c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(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(69,a,110,a)].
% 1.69/1.93 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),A)),B,tc_Int_Oint). [resolve(69,a,111,a)].
% 1.69/1.93 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),C,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(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),C),A,tc_Int_Oint). [resolve(69,a,113,a)].
% 1.69/1.93 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),B,tc_Int_Oint). [resolve(69,a,114,a)].
% 1.69/1.93 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),B)) = hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)). [resolve(69,a,116,a)].
% 1.69/1.93 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(69,a,117,a)].
% 1.69/1.93 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(69,a,118,a)].
% 1.69/1.93 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),B) = hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(69,a,119,a)].
% 1.69/1.93 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,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(69,a,120,a)].
% 1.69/1.93 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(69,a,121,a)].
% 1.69/1.93 Derived: c_Parity_Oeven__odd__class_Oeven(A,tc_nat) | c_lessequals(B,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(69,a,122,a)].
% 1.69/1.93 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A). [resolve(69,a,125,a)].
% 1.69/1.93 Derived: hAPP(c_HOL_Oabs__class_Oabs(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),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)). [resolve(69,a,126,a)].
% 1.69/1.93 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(69,a,127,a)].
% 1.69/1.93 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(69,a,128,a)].
% 1.69/1.93 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint)) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(69,a,129,a)].
% 1.69/1.93 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(69,a,130,a)].
% 1.69/1.93 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(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),C,tc_Int_Oint). [resolve(69,a,131,a)].
% 1.69/1.93 Derived: c_Parity_Oeven__odd__class_Oeven(A,tc_nat) | c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint) | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),A),tc_Int_Oint). [resolve(69,a,134,a)].
% 1.69/1.93 Derived: c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint). [resolve(69,a,139,a)].
% 1.69/1.93 Derived: c_HOL_Oord__class_Oless(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(69,a,140,a)].
% 1.69/1.93 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint)),A)) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(69,a,141,a)].
% 1.69/1.93 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(69,a,142,a)].
% 1.69/1.93 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(69,a,143,a)].
% 1.69/1.93 Derived: hAPP(c_HOL_Oabs__class_Oabs(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),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),B). [resolve(69,a,144,a)].
% 1.69/1.93 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(69,a,147,a)].
% 1.69/1.93 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(69,a,148,a)].
% 1.69/1.93 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),hAPP(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(69,a,149,a)].
% 1.69/1.93 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(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(69,a,150,a)].
% 1.69/1.93 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(69,a,151,a)].
% 1.69/1.93 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(69,a,152,a)].
% 1.69/1.93 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(69,a,153,a)].
% 1.69/1.93 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(69,a,154,a)].
% 1.69/1.93 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(69,a,155,a)].
% 1.69/1.94 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(69,a,156,a)].
% 1.69/1.94 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(69,a,157,a)].
% 1.69/1.94 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(69,a,158,a)].
% 1.69/1.94 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(69,a,159,a)].
% 1.69/1.94 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(69,a,160,a)].
% 1.69/1.94 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(69,a,161,a)].
% 1.69/1.94 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(69,a,162,a)].
% 1.69/1.94 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(69,a,164,a)].
% 1.69/1.94 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(69,a,165,a)].
% 1.69/1.94 Derived: hAPP(c_HOL_Oabs__class_Oabs(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),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(69,a,166,a)].
% 1.69/1.94 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(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),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(69,a,167,a)].
% 1.69/1.94 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(69,a,168,a)].
% 1.74/1.99 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(69,a,169,a)].
% 1.74/1.99 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(69,a,170,a)].
% 1.74/1.99 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(69,a,171,a)].
% 1.74/1.99 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(69,a,172,a)].
% 1.74/1.99 173 class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs) # label(axiom). [assumption].
% 1.74/1.99 174 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = B | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__of__nonneg_0) # label(axiom). [assumption].
% 1.74/1.99 175 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__le__zero__iff_0) # label(axiom). [assumption].
% 1.74/1.99 176 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),B),C,A) # label(cls_abs__le__D2_0) # label(axiom). [assumption].
% 1.74/1.99 177 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C)),hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),A) # label(cls_abs__triangle__ineq2_0) # label(axiom). [assumption].
% 1.74/1.99 178 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)) = hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),B)) # label(cls_abs__minus__commute_0) # label(axiom). [assumption].
% 1.74/1.99 179 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = hAPP(c_HOL_Ouminus__class_Ouminus(A),B) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__of__neg_0) # label(axiom). [assumption].
% 1.74/1.99 180 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(A),B,A,A,C),D,C,A)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(A),B,A,A,C),D,C,A) # label(cls_abs__setsum__abs_0) # label(axiom). [assumption].
% 1.74/1.99 181 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__minus__le__zero_0) # label(axiom). [assumption].
% 1.74/1.99 182 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),B),C,A) # label(cls_abs__le__D1_0) # label(axiom). [assumption].
% 1.74/1.99 183 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),c_Finite__Set_Osetsum(B,C,D,A)),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(A),B,A,A,D),C,D,A),A) # label(cls_setsum__abs_0) # label(axiom). [assumption].
% 1.74/1.99 184 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C))),hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),A) # label(cls_abs__triangle__ineq3_0) # label(axiom). [assumption].
% 1.74/1.99 185 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_abs__eq__0_1) # label(axiom). [assumption].
% 1.74/1.99 186 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C)),A) # label(cls_abs__triangle__ineq_0) # label(axiom). [assumption].
% 1.74/1.99 187 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),B),C,A) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_lessequals(B,C,A) # label(cls_abs__leI_0) # label(axiom). [assumption].
% 1.74/1.99 188 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),B),C,A) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_lessequals(B,C,A) # label(cls_abs__le__iff_2) # label(axiom). [assumption].
% 1.74/1.99 189 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = hAPP(c_HOL_Oabs__class_Oabs(A),B) # label(cls_abs__minus__cancel_0) # label(axiom). [assumption].
% 1.74/1.99 190 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__le__zero__iff_1) # label(axiom). [assumption].
% 1.74/1.99 191 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(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(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D))),hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E))),A) # label(cls_abs__diff__triangle__ineq_0) # label(axiom). [assumption].
% 1.74/1.99 192 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = B | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_abs__of__pos_0) # label(axiom). [assumption].
% 1.74/1.99 193 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = hAPP(c_HOL_Ouminus__class_Ouminus(A),B) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__of__nonpos_0) # label(axiom). [assumption].
% 1.74/1.99 194 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)) = hAPP(c_HOL_Oabs__class_Oabs(A),B) # label(cls_abs__idempotent_0) # label(axiom). [assumption].
% 1.74/1.99 195 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Oabs__class_Oabs(A),B),A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_zero__less__abs__iff_1) # label(axiom). [assumption].
% 1.74/1.99 196 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),hAPP(c_HOL_Oabs__class_Oabs(A),B),A) # label(cls_abs__ge__minus__self_0) # label(axiom). [assumption].
% 1.74/1.99 197 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(B,hAPP(c_HOL_Oabs__class_Oabs(A),B),A) # label(cls_abs__ge__self_0) # label(axiom). [assumption].
% 1.74/1.99 198 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(A),B,A,A,C),D,C,A),A) # label(cls_setsum__abs__ge__zero_0) # label(axiom). [assumption].
% 1.74/1.99 199 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(A),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__not__less__zero_0) # label(axiom). [assumption].
% 1.74/1.99 200 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C)),A) # label(cls_abs__triangle__ineq4_0) # label(axiom). [assumption].
% 1.74/1.99 201 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_abs__eq__0_0) # label(axiom). [assumption].
% 1.74/1.99 202 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Oabs__class_Oabs(A),c_HOL_Ozero__class_Ozero(A)),A) # label(cls_zero__less__abs__iff_0) # label(axiom). [assumption].
% 1.74/1.99 203 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C)) # label(cls_abs__add__abs_0) # label(axiom). [assumption].
% 1.74/1.99 204 -class_OrderedGroup_Opordered__ab__group__add__abs(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Oabs__class_Oabs(A),B),A) # label(cls_abs__ge__zero_0) # label(axiom). [assumption].
% 1.74/1.99 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) = A | -c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(173,a,174,a)].
% 1.74/1.99 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(173,a,175,a)].
% 1.74/1.99 Derived: c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),B,tc_Int_Oint) | -c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),B,tc_Int_Oint). [resolve(173,a,176,a)].
% 1.74/1.99 Derived: c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),tc_Int_Oint). [resolve(173,a,177,a)].
% 1.74/1.99 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)) = hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),A)). [resolve(173,a,178,a)].
% 1.74/1.99 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(173,a,179,a)].
% 1.74/1.99 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A,tc_Int_Oint,tc_Int_Oint,B),C,B,tc_Int_Oint)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A,tc_Int_Oint,tc_Int_Oint,B),C,B,tc_Int_Oint). [resolve(173,a,180,a)].
% 1.74/1.99 Derived: c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(173,a,181,a)].
% 1.74/1.99 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),B,tc_Int_Oint). [resolve(173,a,182,a)].
% 1.74/1.99 Derived: c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_Finite__Set_Osetsum(A,B,C,tc_Int_Oint)),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A,tc_Int_Oint,tc_Int_Oint,C),B,C,tc_Int_Oint),tc_Int_Oint). [resolve(173,a,183,a)].
% 1.74/1.99 Derived: c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B))),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),tc_Int_Oint). [resolve(173,a,184,a)].
% 1.74/2.00 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(173,a,185,a)].
% 1.74/2.00 Derived: c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(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),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)),tc_Int_Oint). [resolve(173,a,186,a)].
% 1.74/2.00 Derived: c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),B,tc_Int_Oint) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),B,tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(173,a,187,a)].
% 1.74/2.00 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)) = hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A). [resolve(173,a,189,a)].
% 1.74/2.00 Derived: c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(173,a,190,a)].
% 1.74/2.00 Derived: c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(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(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),C))),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),D))),tc_Int_Oint). [resolve(173,a,191,a)].
% 1.74/2.00 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) = A | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(173,a,192,a)].
% 1.74/2.00 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(173,a,193,a)].
% 1.74/2.00 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)) = hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A). [resolve(173,a,194,a)].
% 1.74/2.00 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(173,a,195,a)].
% 1.74/2.00 Derived: c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint). [resolve(173,a,196,a)].
% 1.74/2.00 Derived: c_lessequals(A,hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint). [resolve(173,a,197,a)].
% 1.74/2.00 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A,tc_Int_Oint,tc_Int_Oint,B),C,B,tc_Int_Oint),tc_Int_Oint). [resolve(173,a,198,a)].
% 1.74/2.00 Derived: -c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(173,a,199,a)].
% 1.74/2.00 Derived: c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)),tc_Int_Oint). [resolve(173,a,200,a)].
% 1.74/2.00 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(173,a,201,a)].
% 1.74/2.00 Derived: -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),tc_Int_Oint). [resolve(173,a,202,a)].
% 1.74/2.00 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)). [resolve(173,a,203,a)].
% 1.74/2.00 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A),tc_Int_Oint). [resolve(173,a,204,a)].
% 1.81/2.05 205 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.81/2.05 206 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(C,B,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 1.81/2.05 207 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 1.81/2.05 208 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 1.81/2.05 209 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 1.81/2.05 210 -class_Orderings_Olinorder(A) | B = C | -c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 1.81/2.05 211 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 1.81/2.05 212 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = hAPP(c_HOL_Ouminus__class_Ouminus(A),B) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if__lattice_0) # label(axiom). [assumption].
% 1.81/2.05 213 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_not__leE_0) # label(axiom). [assumption].
% 1.81/2.05 214 -class_Orderings_Olinorder(A) | -c_lessequals(B,B,A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 1.81/2.05 215 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,B,A) | c_lessequals(B,B,A) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 1.81/2.05 216 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(C,B,A) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 1.81/2.05 217 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 1.81/2.05 218 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 1.81/2.05 219 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 1.81/2.05 220 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.81/2.05 221 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) | -c_lessequals(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_le__number__of__eq__not__less_0) # label(axiom). [assumption].
% 1.81/2.05 222 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A) | c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_le__number__of__eq__not__less_1) # label(axiom). [assumption].
% 1.81/2.05 223 -class_Orderings_Olinorder(A) | -class_OrderedGroup_Olordered__ab__group__add__abs(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = B | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if__lattice_1) # label(axiom). [assumption].
% 1.81/2.05 224 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 1.81/2.05 225 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 1.81/2.05 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(205,a,206,a)].
% 1.92/2.18 Derived: A = B | -c_lessequals(A,B,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(205,a,210,a)].
% 1.92/2.18 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_nat) | hAPP(c_HOL_Oabs__class_Oabs(tc_nat),A) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_nat),A) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(205,a,212,a)].
% 1.92/2.18 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(205,a,213,a)].
% 1.92/2.18 Derived: -c_lessequals(A,A,tc_nat) | -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(205,a,214,a)].
% 1.92/2.18 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(205,a,216,a)].
% 1.92/2.18 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(205,a,220,a)].
% 1.92/2.18 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_nat) | hAPP(c_HOL_Oabs__class_Oabs(tc_nat),A) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(205,a,223,a)].
% 1.92/2.18 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(205,a,224,a)].
% 1.92/2.18 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(205,a,225,a)].
% 1.92/2.18 226 class_Orderings_Olinorder(tc_Int_Oint) # label(clsarity_Int__Oint__Orderings_Olinorder) # label(axiom). [assumption].
% 1.92/2.18 Derived: A = B | -c_lessequals(A,B,tc_Int_Oint) | c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(226,a,210,a)].
% 1.92/2.18 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | c_lessequals(B,A,tc_Int_Oint). [resolve(226,a,213,a)].
% 1.92/2.18 Derived: -c_lessequals(A,A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,A,tc_Int_Oint). [resolve(226,a,214,a)].
% 1.92/2.18 Derived: -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_lessequals(B,A,tc_Int_Oint). [resolve(226,a,216,a)].
% 1.92/2.18 Derived: -c_HOL_Oord__class_Oless(A,A,tc_Int_Oint). [resolve(226,a,220,a)].
% 1.92/2.18 Derived: -class_OrderedGroup_Olordered__ab__group__add__abs(tc_Int_Oint) | hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(226,a,223,a)].
% 1.92/2.18 Derived: c_lessequals(A,B,tc_Int_Oint) | c_lessequals(B,A,tc_Int_Oint). [resolve(226,a,224,a)].
% 1.92/2.18 Derived: -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,A,tc_Int_Oint). [resolve(226,a,225,a)].
% 1.92/2.18 227 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption].
% 1.92/2.18 228 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__algebra__1(B) | C = D | -c_Lim_OLIM(E,F,D,B,A) | -c_Lim_OLIM(E,F,C,B,A) # label(cls_LIM__unique_0) # label(axiom). [assumption].
% 1.92/2.18 Derived: -class_RealVector_Ometric__space(A) | B = C | -c_Lim_OLIM(D,E,C,tc_Complex_Ocomplex,A) | -c_Lim_OLIM(D,E,B,tc_Complex_Ocomplex,A). [resolve(227,a,228,b)].
% 1.92/2.18 229 class_OrderedGroup_Ogroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 1.92/2.18 230 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),B) != hAPP(c_HOL_Ouminus__class_Ouminus(A),C) | B = C # label(cls_neg__equal__iff__equal_0) # label(axiom). [assumption].
% 1.92/2.18 231 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),B) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__0__iff__equal_0) # label(axiom). [assumption].
% 1.92/2.18 232 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus__eq_1) # label(axiom). [assumption].
% 1.92/2.18 233 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_diff__0__right_0) # label(axiom). [assumption].
% 1.92/2.18 234 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_diff__self_0) # label(axiom). [assumption].
% 1.92/2.18 235 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) != hAPP(c_HOL_Ouminus__class_Ouminus(A),B) | c_HOL_Ozero__class_Ozero(A) = B # label(cls_neg__0__equal__iff__equal_0) # label(axiom). [assumption].
% 1.92/2.18 236 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_HOL_Ozero__class_Ozero(A)),B) = hAPP(c_HOL_Ouminus__class_Ouminus(A),B) # label(cls_group__add__class_Odiff__0_0) # label(axiom). [assumption].
% 1.92/2.18 237 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) # label(cls_diff__minus_0) # label(axiom). [assumption].
% 1.92/2.18 238 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__neg__iff__add__eq__0_0) # label(axiom). [assumption].
% 1.92/2.18 239 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus_0) # label(axiom). [assumption].
% 1.92/2.18 240 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_left__minus_0) # label(axiom). [assumption].
% 1.92/2.18 241 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_right__minus__eq_0) # label(axiom). [assumption].
% 1.92/2.18 242 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) # label(cls_diff__minus__eq__add_0) # label(axiom). [assumption].
% 1.92/2.18 243 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = B # label(cls_minus__equation__iff_1) # label(axiom). [assumption].
% 1.92/2.18 244 -class_OrderedGroup_Ogroup__add(A) | B = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) # label(cls_equation__minus__iff_1) # label(axiom). [assumption].
% 1.92/2.18 245 -class_OrderedGroup_Ogroup__add(A) | B = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) # label(cls_equation__minus__iff_0) # label(axiom). [assumption].
% 1.92/2.18 246 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = B # label(cls_minus__minus_0) # label(axiom). [assumption].
% 1.92/2.18 247 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),B) = C # label(cls_minus__unique_0) # label(axiom). [assumption].
% 1.92/2.18 248 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = hAPP(c_HOL_Ouminus__class_Ouminus(A),C) # label(cls_eq__neg__iff__add__eq__0_1) # label(axiom). [assumption].
% 1.92/2.18 249 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ozero__class_Ozero(A) = hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Ozero__class_Ozero(A)) # label(cls_neg__0__equal__iff__equal_1) # label(axiom). [assumption].
% 1.92/2.18 250 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_minus__zero_0) # label(axiom). [assumption].
% 1.92/2.18 251 -class_OrderedGroup_Ogroup__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) # label(cls_minus__add_0) # label(axiom). [assumption].
% 1.92/2.18 252 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)) = C # label(cls_minus__add__cancel_0) # label(axiom). [assumption].
% 1.92/2.18 253 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C)) = C # label(cls_add__minus__cancel_0) # label(axiom). [assumption].
% 1.92/2.18 254 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),C) = B # label(cls_diff__add__cancel_0) # label(axiom). [assumption].
% 1.92/2.18 255 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),C) = B # label(cls_add__diff__cancel_0) # label(axiom). [assumption].
% 1.92/2.18 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B) | A = B. [resolve(229,a,230,a)].
% 1.92/2.18 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(229,a,231,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(229,a,232,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(229,a,233,a)].
% 1.92/2.18 Derived: c_HOL_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A) | c_HOL_Ozero__class_Ozero(tc_Int_Oint) = A. [resolve(229,a,235,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A). [resolve(229,a,236,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B)). [resolve(229,a,237,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(229,a,238,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(229,a,239,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = B. [resolve(229,a,241,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B). [resolve(229,a,242,a)].
% 1.92/2.18 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)) = A. [resolve(229,a,243,a)].
% 1.92/2.18 Derived: A = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)). [resolve(229,a,244,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A) = B. [resolve(229,a,247,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B). [resolve(229,a,248,a)].
% 1.92/2.18 Derived: c_HOL_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)). [resolve(229,a,249,a)].
% 1.92/2.18 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(229,a,250,a)].
% 1.92/2.18 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(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),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)). [resolve(229,a,251,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)) = B. [resolve(229,a,252,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),B)) = B. [resolve(229,a,253,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),B) = A. [resolve(229,a,254,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),B) = A. [resolve(229,a,255,a)].
% 1.92/2.18 256 class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 1.92/2.18 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B) | A = B. [resolve(256,a,230,a)].
% 1.92/2.18 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(256,a,231,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(256,a,232,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(256,a,233,a)].
% 1.92/2.18 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = A. [resolve(256,a,235,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A). [resolve(256,a,236,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)). [resolve(256,a,237,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(256,a,238,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(256,a,239,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(256,a,241,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B). [resolve(256,a,242,a)].
% 1.92/2.18 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)) = A. [resolve(256,a,243,a)].
% 1.92/2.18 Derived: A = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)). [resolve(256,a,244,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A) = B. [resolve(256,a,247,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B). [resolve(256,a,248,a)].
% 1.92/2.18 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(256,a,249,a)].
% 1.92/2.18 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(256,a,250,a)].
% 1.92/2.18 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(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),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)). [resolve(256,a,251,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)) = B. [resolve(256,a,252,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),B)) = B. [resolve(256,a,253,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)),B) = A. [resolve(256,a,254,a)].
% 1.92/2.18 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),B)),B) = A. [resolve(256,a,255,a)].
% 2.04/2.30 257 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) # label(axiom). [assumption].
% 2.04/2.30 258 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OZseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(A),B,A,A,tc_nat),A) | -c_SEQ_OZseq(B,A) # label(cls_Zseq__minus_0) # label(axiom). [assumption].
% 2.04/2.30 259 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(C,D,E,B,A) | -c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(A),C,A,tc_fun(A,A),B),E,B,A,A),D,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_LIM__zero__iff_0) # label(axiom). [assumption].
% 2.04/2.30 260 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(A),C,A,tc_fun(A,A),B),D,B,A,A),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(C,E,D,B,A) # label(cls_LIM__zero_0) # label(axiom). [assumption].
% 2.04/2.30 261 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OBseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(A),B,A,A,tc_nat),A) | -c_SEQ_OBseq(B,A) # label(cls_Bseq__minus__iff_1) # label(axiom). [assumption].
% 2.04/2.30 262 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OBseq(B,A) | -c_SEQ_OBseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(A),B,A,A,tc_nat),A) # label(cls_Bseq__minus__iff_0) # label(axiom). [assumption].
% 2.04/2.30 263 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osummable(c_COMBB(c_HOL_Ouminus__class_Ouminus(A),B,A,A,tc_nat),A) | -c_Series_Osummable(B,A) # label(cls_summable__minus_0) # label(axiom). [assumption].
% 2.04/2.30 264 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBB(C,hAPP(c_HOL_Oplus__class_Oplus(A),D),A,B,A),c_HOL_Ozero__class_Ozero(A),hAPP(C,D),A,B) | -c_Lim_OisCont(C,D,A,B) # label(cls_isCont__iff_0) # label(axiom). [assumption].
% 2.04/2.30 265 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OisCont(C,D,A,B) | -c_Lim_OLIM(c_COMBB(C,hAPP(c_HOL_Oplus__class_Oplus(A),D),A,B,A),c_HOL_Ozero__class_Ozero(A),hAPP(C,D),A,B) # label(cls_isCont__iff_1) # label(axiom). [assumption].
% 2.04/2.30 266 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OBseq(B,A) | -c_SEQ_OCauchy(B,A) # label(cls_Cauchy__Bseq_0) # label(axiom). [assumption].
% 2.04/2.30 267 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBB(c_HOL_Ouminus__class_Ouminus(A),C,A,A,B),D,hAPP(c_HOL_Ouminus__class_Ouminus(A),E),B,A) | -c_Lim_OLIM(C,D,E,B,A) # label(cls_LIM__minus_0) # label(axiom). [assumption].
% 2.04/2.30 268 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OZseq(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),A) | -c_SEQ_OLIMSEQ(B,C,A) # label(cls_LIMSEQ__Zseq__iff_0) # label(axiom). [assumption].
% 2.04/2.30 269 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(B,C,A) | -c_SEQ_OZseq(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),A) # label(cls_LIMSEQ__Zseq__iff_1) # label(axiom). [assumption].
% 2.04/2.30 270 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__vector(B) | c_Lim_OisCont(c_COMBB(c_HOL_Ouminus__class_Ouminus(B),C,B,B,A),D,A,B) | -c_Lim_OisCont(C,D,A,B) # label(cls_isCont__minus_0) # label(axiom). [assumption].
% 2.04/2.30 271 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osummable(B,A) | -c_Series_Osums(B,C,A) # label(cls_sums__summable_0) # label(axiom). [assumption].
% 2.04/2.30 272 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osummable(B,A) | -c_Series_Osums(B,C,A) # label(cls_sums__iff_0) # label(axiom). [assumption].
% 2.04/2.30 273 -class_RealVector_Oreal__normed__vector(A) | hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(A) | c_Series_Osums(B,C,A) | -c_Series_Osums(c_COMBB(B,c_Suc,tc_nat,A,tc_nat),C,A) # label(cls_sums__Suc__imp_0) # label(axiom). [assumption].
% 2.04/2.30 274 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBB(C,hAPP(c_HOL_Oplus__class_Oplus(A),D),A,B,A),c_HOL_Ozero__class_Ozero(A),hAPP(C,D),A,B) | -c_Lim_OLIM(C,D,hAPP(C,D),A,B) # label(cls_LIM__isCont__iff_0) # label(axiom). [assumption].
% 2.04/2.30 275 -class_RealVector_Oreal__normed__vector(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(C,D,hAPP(C,D),A,B) | -c_Lim_OLIM(c_COMBB(C,hAPP(c_HOL_Oplus__class_Oplus(A),D),A,B,A),c_HOL_Ozero__class_Ozero(A),hAPP(C,D),A,B) # label(cls_LIM__isCont__iff_1) # label(axiom). [assumption].
% 2.04/2.30 276 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__vector(B) | c_Lim_OLIM(c_COMBB(C,hAPP(c_HOL_Oplus__class_Oplus(B),D),B,A,B),c_HOL_Ozero__class_Ozero(B),E,B,A) | -c_Lim_OLIM(C,D,E,B,A) # label(cls_LIM__offset__zero_0) # label(axiom). [assumption].
% 2.04/2.30 277 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__vector(B) | c_Lim_OLIM(C,D,E,B,A) | -c_Lim_OLIM(c_COMBB(C,hAPP(c_HOL_Oplus__class_Oplus(B),D),B,A,B),c_HOL_Ozero__class_Ozero(B),E,B,A) # label(cls_LIM__offset__zero__cancel_0) # label(axiom). [assumption].
% 2.04/2.30 278 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osums(c_COMBB(B,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),C,tc_nat,tc_nat,tc_nat),tc_nat,A,tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,A)),A) | -c_Series_Osums(B,D,A) # label(cls_sums__split__initial__segment_0) # label(axiom). [assumption].
% 2.04/2.30 279 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(B,c_HOL_Ozero__class_Ozero(A),A) | -c_Series_Osummable(B,A) # label(cls_summable__LIMSEQ__zero_0) # label(axiom). [assumption].
% 2.04/2.30 280 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osums(c_COMBB(c_HOL_Ouminus__class_Ouminus(A),B,A,A,tc_nat),hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | -c_Series_Osums(B,C,A) # label(cls_sums__minus_0) # label(axiom). [assumption].
% 2.04/2.30 281 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(B,C,A) | -c_SEQ_OLIMSEQ(c_COMBB(c_HOL_Ouminus__class_Ouminus(A),B,A,A,tc_nat),hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) # label(cls_LIMSEQ__minus__cancel_0) # label(axiom). [assumption].
% 2.04/2.30 282 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(c_COMBB(c_HOL_Ouminus__class_Ouminus(A),B,A,A,tc_nat),hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | -c_SEQ_OLIMSEQ(B,C,A) # label(cls_LIMSEQ__minus_0) # label(axiom). [assumption].
% 2.04/2.30 283 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osums(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat))),A) | -c_Series_Osums(c_COMBB(B,c_Suc,tc_nat,A,tc_nat),C,A) # label(cls_sums__Suc_0) # label(axiom). [assumption].
% 2.04/2.30 284 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),C),A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__diff__const_0) # label(axiom). [assumption].
% 2.04/2.30 285 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__vector(B) | c_Lim_OLIM(c_COMBB(C,c_COMBC(c_HOL_Oplus__class_Oplus(B),D,B,B,B),B,A,B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(B),E),D),F,B,A) | -c_Lim_OLIM(C,E,F,B,A) # label(cls_LIM__offset_0) # label(axiom). [assumption].
% 2.04/2.30 286 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OLIMSEQ(c_COMBC(c_COMBB(c_HOL_Oplus__class_Oplus(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__add__const_0) # label(axiom). [assumption].
% 2.04/2.30 287 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OBseq(B,A) | -c_SEQ_OBseq(c_COMBB(B,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),C,tc_nat,tc_nat,tc_nat),tc_nat,A,tc_nat),A) # label(cls_Bseq__offset_0) # label(axiom). [assumption].
% 2.04/2.30 288 -class_RealVector_Oreal__normed__vector(A) | c_SEQ_OBseq(c_COMBB(B,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),C,tc_nat,tc_nat,tc_nat),tc_nat,A,tc_nat),A) | -c_SEQ_OBseq(B,A) # label(cls_Bseq__ignore__initial__segment_0) # label(axiom). [assumption].
% 2.04/2.30 289 -class_RealVector_Oreal__normed__vector(A) | c_Series_Osummable(c_COMBB(B,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),C,tc_nat,tc_nat,tc_nat),tc_nat,A,tc_nat),A) | -c_Series_Osummable(B,A) # label(cls_summable__ignore__initial__segment_0) # label(axiom). [assumption].
% 2.04/2.30 Derived: c_SEQ_OZseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) | -c_SEQ_OZseq(A,tc_Complex_Ocomplex). [resolve(257,a,258,a)].
% 2.04/2.30 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(B,C,D,A,tc_Complex_Ocomplex) | -c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),D,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(257,a,259,a)].
% 2.04/2.30 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,C,A,tc_Complex_Ocomplex). [resolve(257,a,260,a)].
% 2.04/2.30 Derived: c_SEQ_OBseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) | -c_SEQ_OBseq(A,tc_Complex_Ocomplex). [resolve(257,a,261,a)].
% 2.04/2.30 Derived: c_SEQ_OBseq(A,tc_Complex_Ocomplex) | -c_SEQ_OBseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex). [resolve(257,a,262,a)].
% 2.04/2.30 Derived: c_Series_Osummable(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(257,a,263,a)].
% 2.04/2.30 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBB(B,hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),tc_Complex_Ocomplex,A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(B,C),tc_Complex_Ocomplex,A) | -c_Lim_OisCont(B,C,tc_Complex_Ocomplex,A). [resolve(257,a,264,a)].
% 2.04/2.30 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OisCont(B,C,tc_Complex_Ocomplex,A) | -c_Lim_OLIM(c_COMBB(B,hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),tc_Complex_Ocomplex,A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(B,C),tc_Complex_Ocomplex,A). [resolve(257,a,265,a)].
% 2.04/2.30 Derived: c_SEQ_OBseq(A,tc_Complex_Ocomplex) | -c_SEQ_OCauchy(A,tc_Complex_Ocomplex). [resolve(257,a,266,a)].
% 2.04/2.30 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,A),C,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),D),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,C,D,A,tc_Complex_Ocomplex). [resolve(257,a,267,a)].
% 2.04/2.30 Derived: c_SEQ_OZseq(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex). [resolve(257,a,268,a)].
% 2.04/2.30 Derived: c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex) | -c_SEQ_OZseq(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex). [resolve(257,a,269,a)].
% 2.04/2.30 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OisCont(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,A),C,A,tc_Complex_Ocomplex) | -c_Lim_OisCont(B,C,A,tc_Complex_Ocomplex). [resolve(257,a,270,b)].
% 2.04/2.30 Derived: c_Series_Osummable(A,tc_Complex_Ocomplex) | -c_Series_Osums(A,B,tc_Complex_Ocomplex). [resolve(257,a,271,a)].
% 2.04/2.30 Derived: hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | c_Series_Osums(A,B,tc_Complex_Ocomplex) | -c_Series_Osums(c_COMBB(A,c_Suc,tc_nat,tc_Complex_Ocomplex,tc_nat),B,tc_Complex_Ocomplex). [resolve(257,a,273,a)].
% 2.04/2.30 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBB(B,hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),tc_Complex_Ocomplex,A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(B,C),tc_Complex_Ocomplex,A) | -c_Lim_OLIM(B,C,hAPP(B,C),tc_Complex_Ocomplex,A). [resolve(257,a,274,a)].
% 2.04/2.30 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(B,C,hAPP(B,C),tc_Complex_Ocomplex,A) | -c_Lim_OLIM(c_COMBB(B,hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),tc_Complex_Ocomplex,A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(B,C),tc_Complex_Ocomplex,A). [resolve(257,a,275,a)].
% 2.04/2.30 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBB(B,hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),tc_Complex_Ocomplex,A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),D,tc_Complex_Ocomplex,A) | -c_Lim_OLIM(B,C,D,tc_Complex_Ocomplex,A). [resolve(257,a,276,b)].
% 2.04/2.30 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(B,C,D,tc_Complex_Ocomplex,A) | -c_Lim_OLIM(c_COMBB(B,hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),tc_Complex_Ocomplex,A,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),D,tc_Complex_Ocomplex,A). [resolve(257,a,277,b)].
% 2.04/2.30 Derived: c_Series_Osums(c_COMBB(A,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),B,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat,tc_Complex_Ocomplex)),tc_Complex_Ocomplex) | -c_Series_Osums(A,C,tc_Complex_Ocomplex). [resolve(257,a,278,a)].
% 2.04/2.30 Derived: c_SEQ_OLIMSEQ(A,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(257,a,279,a)].
% 2.04/2.30 Derived: c_Series_Osums(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B),tc_Complex_Ocomplex) | -c_Series_Osums(A,B,tc_Complex_Ocomplex). [resolve(257,a,280,a)].
% 2.04/2.30 Derived: c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B),tc_Complex_Ocomplex). [resolve(257,a,281,a)].
% 2.04/2.30 Derived: c_SEQ_OLIMSEQ(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,B,tc_Complex_Ocomplex). [resolve(257,a,282,a)].
% 2.04/2.30 Derived: c_Series_Osums(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))),tc_Complex_Ocomplex) | -c_Series_Osums(c_COMBB(A,c_Suc,tc_nat,tc_Complex_Ocomplex,tc_nat),B,tc_Complex_Ocomplex). [resolve(257,a,283,a)].
% 2.04/2.30 Derived: c_SEQ_OLIMSEQ(c_COMBC(c_COMBB(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(257,a,284,a)].
% 2.04/2.30 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBB(B,c_COMBC(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex,A,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),D),C),E,tc_Complex_Ocomplex,A) | -c_Lim_OLIM(B,D,E,tc_Complex_Ocomplex,A). [resolve(257,a,285,b)].
% 2.04/2.30 Derived: c_SEQ_OLIMSEQ(c_COMBC(c_COMBB(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(257,a,286,a)].
% 2.04/2.30 Derived: c_SEQ_OBseq(A,tc_Complex_Ocomplex) | -c_SEQ_OBseq(c_COMBB(A,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),B,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex). [resolve(257,a,287,a)].
% 2.13/2.38 Derived: c_SEQ_OBseq(c_COMBB(A,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),B,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) | -c_SEQ_OBseq(A,tc_Complex_Ocomplex). [resolve(257,a,288,a)].
% 2.13/2.38 Derived: c_Series_Osummable(c_COMBB(A,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),B,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(257,a,289,a)].
% 2.13/2.38 290 class_Divides_Osemiring__div(tc_nat) # label(clsarity_nat__Divides_Osemiring__div) # label(axiom). [assumption].
% 2.13/2.38 291 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),C,A) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self2__is__id_0) # label(axiom). [assumption].
% 2.13/2.38 292 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),B,A) = C | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self1__is__id_0) # label(axiom). [assumption].
% 2.13/2.38 293 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),C),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult1__if_0) # label(axiom). [assumption].
% 2.13/2.38 294 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) = c_Divides_Odiv__class_Odiv(C,D,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult1_0) # label(axiom). [assumption].
% 2.13/2.38 295 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) = c_Divides_Odiv__class_Odiv(B,D,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult2_0) # label(axiom). [assumption].
% 2.13/2.38 296 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__by__0_0) # label(axiom). [assumption].
% 2.13/2.38 297 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__0_0) # label(axiom). [assumption].
% 2.13/2.38 298 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__self_0) # label(axiom). [assumption].
% 2.13/2.38 299 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),C,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),c_Divides_Odiv__class_Odiv(B,C,A)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self2_0) # label(axiom). [assumption].
% 2.13/2.38 300 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),D,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),c_Divides_Odiv__class_Odiv(B,D,A)) | D = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self1_0) # label(axiom). [assumption].
% 2.13/2.38 301 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),C,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Odiv(B,C,A)),c_HOL_Oone__class_Oone(A)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__add__self2_0) # label(axiom). [assumption].
% 2.13/2.38 302 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),B,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Odiv(C,B,A)),c_HOL_Oone__class_Oone(A)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__add__self1_0) # label(axiom). [assumption].
% 2.13/2.38 303 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Oone__class_Oone(A),A) = B # label(cls_div__by__1_0) # label(axiom). [assumption].
% 2.13/2.38 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),B,tc_nat) = A | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(290,a,291,a)].
% 2.13/2.38 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),A,tc_nat) = B | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(290,a,292,a)].
% 2.13/2.38 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(290,a,293,a)].
% 2.13/2.38 Derived: c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(B,C,tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(290,a,294,a)].
% 2.13/2.38 Derived: c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(A,C,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(290,a,295,a)].
% 2.13/2.38 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(290,a,296,a)].
% 2.13/2.38 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(290,a,297,a)].
% 2.13/2.38 Derived: c_Divides_Odiv__class_Odiv(A,A,tc_nat) = c_HOL_Oone__class_Oone(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(290,a,298,a)].
% 2.13/2.38 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)),B,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_Divides_Odiv__class_Odiv(A,B,tc_nat)) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(290,a,299,a)].
% 2.13/2.38 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)),C,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_Divides_Odiv__class_Odiv(A,C,tc_nat)) | C = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(290,a,300,a)].
% 2.13/2.38 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(290,a,301,a)].
% 2.13/2.38 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(B,A,tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(290,a,302,a)].
% 2.13/2.38 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = A. [resolve(290,a,303,a)].
% 2.13/2.38 304 class_Divides_Osemiring__div(tc_Int_Oint) # label(clsarity_Int__Oint__Divides_Osemiring__div) # label(axiom). [assumption].
% 2.13/2.38 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),B,tc_Int_Oint) = A | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(304,a,291,a)].
% 2.13/2.38 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),A,tc_Int_Oint) = B | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(304,a,292,a)].
% 2.13/2.38 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),B),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(304,a,293,a)].
% 2.13/2.38 Derived: c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(B,C,tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(304,a,294,a)].
% 2.13/2.38 Derived: c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(A,C,tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(304,a,295,a)].
% 2.21/2.47 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(304,a,296,a)].
% 2.21/2.47 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(304,a,297,a)].
% 2.21/2.47 Derived: c_Divides_Odiv__class_Odiv(A,A,tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(304,a,298,a)].
% 2.21/2.47 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)),B,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint)) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(304,a,299,a)].
% 2.21/2.47 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)),C,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),c_Divides_Odiv__class_Odiv(A,C,tc_Int_Oint)) | C = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(304,a,300,a)].
% 2.21/2.47 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),B,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint)),c_HOL_Oone__class_Oone(tc_Int_Oint)) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(304,a,301,a)].
% 2.21/2.47 Derived: c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),A,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Odiv(B,A,tc_Int_Oint)),c_HOL_Oone__class_Oone(tc_Int_Oint)) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(304,a,302,a)].
% 2.21/2.47 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = A. [resolve(304,a,303,a)].
% 2.21/2.47 305 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 2.21/2.47 306 -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].
% 2.21/2.47 307 -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].
% 2.21/2.47 308 -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].
% 2.21/2.47 309 -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].
% 2.21/2.47 310 -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].
% 2.21/2.47 311 -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].
% 2.21/2.47 312 -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].
% 2.21/2.47 313 -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].
% 2.21/2.47 314 -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].
% 2.21/2.47 315 -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].
% 2.21/2.47 316 -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].
% 2.21/2.47 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(305,a,306,a)].
% 2.21/2.47 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(305,a,307,a)].
% 2.21/2.47 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(305,a,308,a)].
% 2.21/2.47 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(305,a,309,a)].
% 2.21/2.47 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(305,a,310,a)].
% 2.21/2.47 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(305,a,311,a)].
% 2.21/2.47 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(305,a,312,a)].
% 2.21/2.47 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(305,a,313,a)].
% 2.21/2.47 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(305,a,314,a)].
% 2.29/2.54 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(305,a,315,a)].
% 2.29/2.54 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(305,a,316,a)].
% 2.29/2.54 317 class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 2.29/2.54 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(317,a,306,a)].
% 2.29/2.54 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(317,a,307,a)].
% 2.29/2.54 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(317,a,308,a)].
% 2.29/2.54 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(317,a,309,a)].
% 2.29/2.54 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(317,a,311,a)].
% 2.29/2.54 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(317,a,312,a)].
% 2.29/2.54 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(317,a,313,a)].
% 2.29/2.54 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(317,a,314,a)].
% 2.29/2.54 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(317,a,315,a)].
% 2.29/2.54 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(317,a,316,a)].
% 2.29/2.54 318 class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 2.29/2.54 319 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_neg__less__iff__less_1) # label(axiom). [assumption].
% 2.29/2.54 320 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_neg__less__iff__less_0) # label(axiom). [assumption].
% 2.29/2.54 321 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__le__0__iff__le_0) # label(axiom). [assumption].
% 2.29/2.54 322 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),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].
% 2.29/2.54 323 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(D,E,A) # label(cls_less__eqI_1) # label(axiom). [assumption].
% 2.29/2.54 324 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | c_HOL_Oord__class_Oless(D,E,A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__eqI_0) # label(axiom). [assumption].
% 2.29/2.54 325 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | c_lessequals(C,B,A) | -c_lessequals(E,D,A) # label(cls_le__eqI_1) # label(axiom). [assumption].
% 2.29/2.54 326 -class_OrderedGroup_Opordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),E) | c_lessequals(E,D,A) | -c_lessequals(C,B,A) # label(cls_le__eqI_0) # label(axiom). [assumption].
% 2.29/2.54 327 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_neg__le__iff__le_0) # label(axiom). [assumption].
% 2.29/2.54 328 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | -c_lessequals(C,B,A) # label(cls_le__imp__neg__le_0) # label(axiom). [assumption].
% 2.29/2.54 329 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),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].
% 2.29/2.54 330 -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(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__less__0__iff__less_0) # label(axiom). [assumption].
% 2.29/2.54 331 -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),hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_neg__0__le__iff__le_0) # label(axiom). [assumption].
% 2.29/2.54 332 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_neg__0__le__iff__le_1) # label(axiom). [assumption].
% 2.29/2.54 333 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),B,A) # label(cls_minus__less__iff_1) # label(axiom). [assumption].
% 2.29/2.54 334 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),B,A) # label(cls_minus__less__iff_0) # label(axiom). [assumption].
% 2.29/2.55 335 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | -c_HOL_Oord__class_Oless(C,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_less__minus__iff_1) # label(axiom). [assumption].
% 2.29/2.55 336 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | -c_HOL_Oord__class_Oless(C,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_less__minus__iff_0) # label(axiom). [assumption].
% 2.29/2.55 337 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),B,A) # label(cls_minus__le__iff_1) # label(axiom). [assumption].
% 2.29/2.55 338 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),C,A) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),C),B,A) # label(cls_minus__le__iff_0) # label(axiom). [assumption].
% 2.29/2.55 339 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | -c_lessequals(C,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_le__minus__iff_1) # label(axiom). [assumption].
% 2.29/2.55 340 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),C),A) | -c_lessequals(C,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_le__minus__iff_0) # label(axiom). [assumption].
% 2.29/2.55 341 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,C,A) # label(cls_le__iff__diff__le__0_0) # label(axiom). [assumption].
% 2.29/2.55 342 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) # label(cls_le__iff__diff__le__0_1) # label(axiom). [assumption].
% 2.29/2.55 343 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__iff__diff__less__0_0) # label(axiom). [assumption].
% 2.29/2.55 344 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),c_HOL_Ozero__class_Ozero(A),A) # label(cls_less__iff__diff__less__0_1) # label(axiom). [assumption].
% 2.29/2.55 345 -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].
% 2.29/2.55 346 -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),hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_neg__0__less__iff__less_0) # label(axiom). [assumption].
% 2.29/2.55 347 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B),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].
% 2.29/2.55 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,A,tc_Int_Oint). [resolve(318,a,319,a)].
% 2.29/2.55 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint). [resolve(318,a,320,a)].
% 2.29/2.55 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(318,a,321,a)].
% 2.29/2.55 Derived: c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),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). [resolve(318,a,322,a)].
% 2.29/2.55 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),D) | c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,D,tc_Int_Oint). [resolve(318,a,323,a)].
% 2.29/2.55 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),D) | c_HOL_Oord__class_Oless(C,D,tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(318,a,324,a)].
% 2.29/2.55 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),D) | c_lessequals(B,A,tc_Int_Oint) | -c_lessequals(D,C,tc_Int_Oint). [resolve(318,a,325,a)].
% 2.29/2.55 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),D) | c_lessequals(D,C,tc_Int_Oint) | -c_lessequals(B,A,tc_Int_Oint). [resolve(318,a,326,a)].
% 2.29/2.55 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint). [resolve(318,a,327,a)].
% 2.29/2.55 Derived: c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B),tc_Int_Oint) | -c_lessequals(B,A,tc_Int_Oint). [resolve(318,a,328,a)].
% 2.29/2.55 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),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). [resolve(318,a,329,a)].
% 2.29/2.55 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(318,a,330,a)].
% 2.29/2.55 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),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint). [resolve(318,a,331,a)].
% 2.29/2.55 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint) | -c_lessequals(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(318,a,332,a)].
% 2.29/2.55 Derived: c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B),A,tc_Int_Oint). [resolve(318,a,333,a)].
% 2.29/2.55 Derived: c_HOL_Oord__class_Oless(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B),tc_Int_Oint) | -c_HOL_Oord__class_Oless(B,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint). [resolve(318,a,335,a)].
% 2.29/2.55 Derived: c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),B,tc_Int_Oint) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B),A,tc_Int_Oint). [resolve(318,a,337,a)].
% 2.29/2.55 Derived: c_lessequals(A,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B),tc_Int_Oint) | -c_lessequals(B,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint). [resolve(318,a,339,a)].
% 2.29/2.55 Derived: c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(318,a,341,a)].
% 2.29/2.55 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(318,a,342,a)].
% 2.29/2.55 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,B,tc_Int_Oint). [resolve(318,a,343,a)].
% 2.29/2.55 Derived: c_HOL_Oord__class_Oless(A,B,tc_Int_Oint) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(318,a,344,a)].
% 2.29/2.55 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(318,a,345,a)].
% 2.41/2.66 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),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint). [resolve(318,a,346,a)].
% 2.41/2.66 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A),tc_Int_Oint) | -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(318,a,347,a)].
% 2.41/2.66 348 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 2.41/2.66 349 -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].
% 2.41/2.66 350 -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].
% 2.41/2.66 351 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Ozero__class_Ozero(A) != c_HOL_Oone__class_Oone(A) # label(cls_zero__neq__one_0) # label(axiom). [assumption].
% 2.41/2.66 352 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Oone__class_Oone(A) != c_HOL_Ozero__class_Ozero(A) # label(cls_one__neq__zero_0) # label(axiom). [assumption].
% 2.41/2.66 353 -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].
% 2.41/2.66 354 -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].
% 2.41/2.66 355 -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].
% 2.41/2.66 356 -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].
% 2.41/2.66 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(348,a,349,a)].
% 2.41/2.66 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(348,a,350,a)].
% 2.41/2.66 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(348,a,351,a)].
% 2.41/2.66 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(348,a,352,a)].
% 2.41/2.66 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(348,a,353,a)].
% 2.41/2.66 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | 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(348,a,356,a)].
% 2.41/2.66 357 class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 2.41/2.66 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | 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(357,a,349,a)].
% 2.41/2.66 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | 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(357,a,350,a)].
% 2.41/2.66 Derived: c_HOL_Ozero__class_Ozero(tc_Int_Oint) != c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(357,a,351,a)].
% 2.41/2.66 Derived: c_HOL_Oone__class_Oone(tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(357,a,352,a)].
% 2.41/2.66 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | 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(357,a,353,a)].
% 2.41/2.66 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(tc_Int_Oint) | -class_Power_Opower(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | 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(357,a,356,a)].
% 2.41/2.66 358 class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 2.41/2.66 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(358,a,349,a)].
% 2.41/2.66 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(358,a,350,a)].
% 2.41/2.66 Derived: c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(358,a,351,a)].
% 2.41/2.66 Derived: c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(358,a,352,a)].
% 2.41/2.66 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(358,a,353,a)].
% 2.41/2.66 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) | -class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) | -class_Power_Opower(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | 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(358,a,356,a)].
% 2.43/2.70 359 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 2.43/2.70 360 -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].
% 2.43/2.70 361 -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)),hAPP(c_Suc,B)) = c_HOL_Ozero__class_Ozero(A) # label(cls_power__0__Suc_0) # label(axiom). [assumption].
% 2.43/2.70 362 -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].
% 2.43/2.70 363 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Finite__Set_Osetsum(C,D,E,A)) = c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A,E),D,E,A) # label(cls_setsum__right__distrib_0) # label(axiom). [assumption].
% 2.43/2.70 364 -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].
% 2.43/2.70 365 -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].
% 2.43/2.70 366 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Finite__Set_Osetsum(B,C,D,A)),E) = c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),D),E,D,A,A),C,D,A) # label(cls_setsum__left__distrib_0) # label(axiom). [assumption].
% 2.43/2.70 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(359,a,360,a)].
% 2.43/2.70 Derived: -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(c_Suc,A)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(359,a,361,a)].
% 2.43/2.70 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(359,a,362,a)].
% 2.43/2.70 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Finite__Set_Osetsum(B,C,D,tc_nat)) = c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B,tc_nat,tc_nat,D),C,D,tc_nat). [resolve(359,a,363,a)].
% 2.43/2.70 Derived: -class_Power_Opower(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat). [resolve(359,a,364,a)].
% 2.43/2.70 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Finite__Set_Osetsum(A,B,C,tc_nat)),D) = c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),A,tc_nat,tc_fun(tc_nat,tc_nat),C),D,C,tc_nat,tc_nat),B,C,tc_nat). [resolve(359,a,366,a)].
% 2.43/2.70 367 class_Ring__and__Field_Osemiring__0(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 2.49/2.73 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(367,a,360,a)].
% 2.49/2.73 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)),hAPP(c_Suc,A)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(367,a,361,a)].
% 2.49/2.73 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(367,a,362,a)].
% 2.49/2.73 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Finite__Set_Osetsum(B,C,D,tc_Int_Oint)) = c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B,tc_Int_Oint,tc_Int_Oint,D),C,D,tc_Int_Oint). [resolve(367,a,363,a)].
% 2.49/2.73 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_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(367,a,364,a)].
% 2.49/2.73 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Finite__Set_Osetsum(A,B,C,tc_Int_Oint)),D) = c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),C),D,C,tc_Int_Oint,tc_Int_Oint),B,C,tc_Int_Oint). [resolve(367,a,366,a)].
% 2.49/2.73 368 class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 2.49/2.73 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(368,a,360,a)].
% 2.49/2.73 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)),hAPP(c_Suc,A)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(368,a,361,a)].
% 2.49/2.73 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(368,a,362,a)].
% 2.49/2.73 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_Finite__Set_Osetsum(B,C,D,tc_Complex_Ocomplex)) = c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,D),C,D,tc_Complex_Ocomplex). [resolve(368,a,363,a)].
% 2.49/2.73 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(368,a,364,a)].
% 2.49/2.73 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Finite__Set_Osetsum(A,B,C,tc_Complex_Ocomplex)),D) = c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),C),D,C,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B,C,tc_Complex_Ocomplex). [resolve(368,a,366,a)].
% 2.49/2.73 369 class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) # label(axiom). [assumption].
% 2.49/2.73 370 -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].
% 2.49/2.73 371 -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].
% 2.49/2.73 372 -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].
% 2.49/2.73 373 -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].
% 2.49/2.73 374 -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].
% 2.49/2.73 375 -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].
% 2.49/2.73 376 -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].
% 2.49/2.73 377 -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].
% 2.49/2.73 378 -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].
% 2.49/2.73 379 -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].
% 2.49/2.73 380 -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].
% 2.49/2.73 381 -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].
% 2.49/2.73 382 -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].
% 2.49/2.73 383 -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].
% 2.49/2.73 384 -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].
% 2.49/2.73 385 -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].
% 2.49/2.73 386 -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].
% 2.49/2.73 387 -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].
% 2.49/2.73 388 -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].
% 2.49/2.73 389 -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].
% 2.49/2.73 390 -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].
% 2.49/2.73 391 -class_Ring__and__Field_Oordered__ring__strict(A) | -class_OrderedGroup_Omonoid__mult(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__even__power_0) # label(axiom). [assumption].
% 2.49/2.73 392 -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].
% 2.49/2.73 393 -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].
% 2.49/2.73 394 -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].
% 2.49/2.73 395 -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].
% 2.49/2.73 396 -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].
% 2.49/2.73 397 -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].
% 2.49/2.73 398 -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].
% 2.49/2.73 399 -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].
% 2.49/2.73 400 -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].
% 2.49/2.73 401 -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].
% 2.49/2.73 402 -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].
% 2.49/2.73 403 -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].
% 2.49/2.73 404 -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].
% 2.49/2.73 405 -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].
% 2.49/2.73 406 -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].
% 2.49/2.73 407 -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].
% 2.49/2.73 408 -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].
% 2.49/2.73 409 -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].
% 2.49/2.73 410 -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].
% 2.49/2.73 411 -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].
% 2.49/2.73 412 -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].
% 2.49/2.73 413 -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].
% 2.49/2.73 414 -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].
% 2.49/2.73 415 -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].
% 2.49/2.73 416 -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].
% 2.49/2.73 417 -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].
% 2.49/2.73 418 -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].
% 2.49/2.73 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(369,a,371,a)].
% 2.49/2.73 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(369,a,372,a)].
% 2.49/2.73 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(369,a,374,a)].
% 2.49/2.73 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(369,a,375,a)].
% 2.49/2.73 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(369,a,376,a)].
% 2.49/2.73 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(369,a,378,a)].
% 2.49/2.73 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(369,a,379,a)].
% 2.49/2.73 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(369,a,381,a)].
% 2.49/2.73 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(369,a,382,a)].
% 2.49/2.73 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(369,a,383,a)].
% 2.49/2.73 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(369,a,384,a)].
% 2.49/2.73 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(369,a,385,a)].
% 2.49/2.73 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(369,a,386,a)].
% 2.49/2.73 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(369,a,387,a)].
% 2.49/2.73 Derived: c_lessequals(A,B,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) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),C,tc_Int_Oint). [resolve(369,a,388,a)].
% 2.49/2.73 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(369,a,389,a)].
% 2.49/2.73 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(369,a,390,a)].
% 2.49/2.73 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(369,a,392,a)].
% 2.49/2.73 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(A,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),B,tc_Int_Oint). [resolve(369,a,393,a)].
% 2.49/2.73 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(369,a,395,a)].
% 2.49/2.73 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(B,C,tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint). [resolve(369,a,396,a)].
% 2.49/2.73 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(369,a,399,a)].
% 2.49/2.73 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(369,a,401,a)].
% 2.49/2.73 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(369,a,402,a)].
% 2.49/2.73 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(369,a,403,a)].
% 2.49/2.73 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(369,a,404,a)].
% 2.49/2.73 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(369,a,405,a)].
% 2.49/2.73 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(369,a,406,a)].
% 2.49/2.73 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(369,a,407,a)].
% 2.49/2.73 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(369,a,408,a)].
% 2.52/2.77 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(369,a,409,a)].
% 2.52/2.77 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(369,a,410,a)].
% 2.52/2.77 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(369,a,411,a)].
% 2.52/2.77 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(369,a,412,a)].
% 2.52/2.77 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(369,a,413,a)].
% 2.52/2.77 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(369,a,414,a)].
% 2.52/2.77 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(369,a,415,a)].
% 2.52/2.77 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(369,a,416,a)].
% 2.52/2.77 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(369,a,417,a)].
% 2.52/2.77 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(369,a,418,a)].
% 2.52/2.77 419 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 2.52/2.77 420 -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].
% 2.52/2.77 421 -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].
% 2.52/2.77 422 -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].
% 2.52/2.77 423 -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].
% 2.52/2.77 424 -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].
% 2.52/2.77 425 -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].
% 2.52/2.77 426 -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].
% 2.52/2.77 427 -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].
% 2.52/2.77 428 -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].
% 2.52/2.77 429 -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].
% 2.52/2.77 430 -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].
% 2.52/2.77 431 -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].
% 2.52/2.77 432 -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].
% 2.52/2.77 433 -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].
% 2.52/2.77 434 -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].
% 2.52/2.77 435 -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].
% 2.52/2.77 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(419,a,420,a)].
% 2.52/2.77 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(419,a,421,a)].
% 2.52/2.77 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(419,a,423,a)].
% 2.52/2.77 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(419,a,424,a)].
% 2.52/2.77 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(419,a,425,a)].
% 2.52/2.77 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(419,a,426,a)].
% 2.52/2.77 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(419,a,427,a)].
% 2.52/2.77 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(419,a,428,a)].
% 2.52/2.77 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(419,a,429,a)].
% 2.52/2.77 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(419,a,430,a)].
% 2.52/2.77 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(419,a,431,a)].
% 2.52/2.77 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(419,a,432,a)].
% 2.52/2.77 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(419,a,433,a)].
% 2.52/2.77 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(419,a,434,a)].
% 2.52/2.77 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(419,a,435,a)].
% 2.52/2.77 436 class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 2.52/2.77 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(436,a,420,a)].
% 2.52/2.77 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(436,a,421,a)].
% 2.52/2.77 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(436,a,423,a)].
% 2.52/2.77 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(436,a,424,a)].
% 2.52/2.77 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(436,a,425,a)].
% 2.52/2.77 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(436,a,426,a)].
% 2.52/2.77 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(436,a,427,a)].
% 2.52/2.77 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(436,a,428,a)].
% 2.52/2.81 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(436,a,429,a)].
% 2.52/2.81 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(436,a,430,a)].
% 2.52/2.81 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(436,a,434,a)].
% 2.52/2.81 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(436,a,435,a)].
% 2.52/2.81 437 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 2.52/2.81 438 -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].
% 2.52/2.81 439 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)) != hAPP(hAPP(c_Power_Opower__class_Opower(A),D),hAPP(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].
% 2.52/2.81 440 -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].
% 2.52/2.81 441 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(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].
% 2.52/2.81 442 -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].
% 2.52/2.81 443 -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].
% 2.52/2.81 444 -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].
% 2.52/2.81 445 -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].
% 2.52/2.81 446 -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].
% 2.52/2.81 447 -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].
% 2.52/2.81 448 -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].
% 2.52/2.81 449 -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),hAPP(c_Suc,D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Suc,D)),A) # label(cls_power__le__imp__le__base_0) # label(axiom). [assumption].
% 2.52/2.81 450 -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].
% 2.52/2.81 451 -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].
% 2.52/2.81 452 -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].
% 2.52/2.81 453 -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].
% 2.52/2.81 454 -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),hAPP(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].
% 2.52/2.81 455 -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].
% 2.52/2.81 456 -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].
% 2.52/2.81 457 -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].
% 2.52/2.81 458 -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].
% 2.52/2.81 459 -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].
% 2.52/2.81 460 -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].
% 2.52/2.81 461 -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].
% 2.52/2.81 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(437,a,438,a)].
% 2.52/2.81 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),hAPP(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(437,a,439,a)].
% 2.52/2.81 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(437,a,440,a)].
% 2.52/2.81 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(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(437,a,441,a)].
% 2.52/2.81 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(437,a,442,a)].
% 2.52/2.81 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(437,a,443,a)].
% 2.52/2.81 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(437,a,444,a)].
% 2.52/2.81 Derived: -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(437,a,445,a)].
% 2.52/2.81 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(437,a,446,a)].
% 2.52/2.81 Derived: -c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(437,a,447,a)].
% 2.52/2.81 Derived: c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(437,a,448,a)].
% 2.52/2.81 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),hAPP(c_Suc,C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),hAPP(c_Suc,C)),tc_nat). [resolve(437,a,449,a)].
% 2.52/2.81 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(437,a,450,a)].
% 2.52/2.81 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(437,a,452,a)].
% 2.52/2.81 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(437,a,453,a)].
% 2.52/2.81 Derived: c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B)),tc_nat) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat). [resolve(437,a,454,a)].
% 2.52/2.81 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(437,a,455,a)].
% 2.52/2.81 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(437,a,456,a)].
% 2.52/2.81 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(437,a,457,a)].
% 2.52/2.81 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(437,a,458,a)].
% 2.52/2.81 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(437,a,459,a)].
% 2.52/2.81 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(437,a,460,a)].
% 2.52/2.81 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(437,a,461,a)].
% 2.52/2.81 462 class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 2.52/2.81 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(462,a,438,a)].
% 2.52/2.81 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Suc,B)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),hAPP(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(462,a,439,a)].
% 2.52/2.81 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(462,a,440,a)].
% 2.52/2.81 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(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(462,a,441,a)].
% 2.52/2.81 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(462,a,443,a)].
% 2.52/2.81 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(462,a,444,a)].
% 2.52/2.81 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(462,a,445,a)].
% 2.52/2.81 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(462,a,446,a)].
% 2.52/2.81 Derived: -c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(462,a,447,a)].
% 2.52/2.81 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(462,a,448,a)].
% 2.52/2.81 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),hAPP(c_Suc,C)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),hAPP(c_Suc,C)),tc_Int_Oint). [resolve(462,a,449,a)].
% 2.52/2.81 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(462,a,450,a)].
% 2.52/2.81 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(462,a,452,a)].
% 2.52/2.81 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(462,a,453,a)].
% 2.52/2.81 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),hAPP(c_Suc,B)),tc_Int_Oint) | -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),A,tc_Int_Oint). [resolve(462,a,454,a)].
% 2.52/2.81 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(462,a,455,a)].
% 2.52/2.81 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(462,a,456,a)].
% 2.52/2.81 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(462,a,457,a)].
% 2.52/2.81 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(462,a,458,a)].
% 2.52/2.81 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(462,a,459,a)].
% 2.52/2.81 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(462,a,460,a)].
% 2.52/2.81 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(462,a,461,a)].
% 2.64/2.91 463 class_Ring__and__Field_Omult__mono1(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 2.64/2.91 464 -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].
% 2.64/2.91 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(463,a,464,a)].
% 2.64/2.91 465 class_Ring__and__Field_Omult__mono1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 2.64/2.91 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(465,a,464,a)].
% 2.64/2.91 466 class_Ring__and__Field_Omult__mono(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 2.64/2.91 467 -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].
% 2.64/2.91 468 -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].
% 2.64/2.91 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(466,a,468,a)].
% 2.64/2.91 469 class_Ring__and__Field_Omult__mono(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 2.64/2.91 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(469,a,468,a)].
% 2.64/2.91 470 class_Ring__and__Field_Opordered__ring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 2.64/2.91 471 -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].
% 2.64/2.91 472 -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].
% 2.64/2.91 473 -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].
% 2.64/2.91 474 -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].
% 2.64/2.91 475 -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].
% 2.64/2.91 476 -class_Ring__and__Field_Opordered__ring(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F),A) | -c_HOL_Oord__class_Oless(D,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B)),C)),F),A) # label(cls_less__add__iff2_1) # label(axiom). [assumption].
% 2.64/2.91 477 -class_Ring__and__Field_Opordered__ring(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)),E)),F),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)),F),A) # label(cls_less__add__iff2_0) # label(axiom). [assumption].
% 2.64/2.91 478 -class_Ring__and__Field_Opordered__ring(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F),A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C)),D),F,A) # label(cls_less__add__iff1_1) # label(axiom). [assumption].
% 2.64/2.91 479 -class_Ring__and__Field_Opordered__ring(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D)),E),F,A) | -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),E),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),F),A) # label(cls_less__add__iff1_0) # label(axiom). [assumption].
% 2.64/2.91 480 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F),A) | -c_lessequals(D,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B)),C)),F),A) # label(cls_le__add__iff2_1) # label(axiom). [assumption].
% 2.64/2.91 481 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)),E)),F),A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)),F),A) # label(cls_le__add__iff2_0) # label(axiom). [assumption].
% 2.64/2.91 482 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F),A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C)),D),F,A) # label(cls_le__add__iff1_1) # label(axiom). [assumption].
% 2.64/2.91 483 -class_Ring__and__Field_Opordered__ring(A) | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D)),E),F,A) | -c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),E),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),F),A) # label(cls_le__add__iff1_0) # label(axiom). [assumption].
% 2.64/2.91 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(470,a,471,a)].
% 2.64/2.91 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(470,a,472,a)].
% 2.64/2.91 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),B)),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),E),tc_Int_Oint) | -c_HOL_Oord__class_Oless(C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E),tc_Int_Oint). [resolve(470,a,476,a)].
% 2.64/2.91 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),C)),D)),E),tc_Int_Oint) | -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),C),D)),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D)),E),tc_Int_Oint). [resolve(470,a,477,a)].
% 2.64/2.91 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),B)),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),E),tc_Int_Oint) | -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),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C),E,tc_Int_Oint). [resolve(470,a,478,a)].
% 2.64/2.91 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),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),C)),D),E,tc_Int_Oint) | -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),C)),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)),E),tc_Int_Oint). [resolve(470,a,479,a)].
% 2.64/2.91 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(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),D),B)),E),tc_Int_Oint) | -c_lessequals(C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E),tc_Int_Oint). [resolve(470,a,480,a)].
% 2.64/2.91 Derived: c_lessequals(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),C)),D)),E),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),C),D)),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D)),E),tc_Int_Oint). [resolve(470,a,481,a)].
% 2.64/2.91 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(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),D),B)),E),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),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C),E,tc_Int_Oint). [resolve(470,a,482,a)].
% 2.64/2.91 Derived: c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),C)),D),E,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),C)),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)),E),tc_Int_Oint). [resolve(470,a,483,a)].
% 2.71/2.98 484 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 2.71/2.98 485 -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].
% 2.71/2.98 486 -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].
% 2.71/2.98 487 -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].
% 2.71/2.98 488 -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].
% 2.71/2.98 489 -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].
% 2.71/2.98 490 -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].
% 2.71/2.98 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(484,a,485,a)].
% 2.71/2.98 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(484,a,486,a)].
% 2.71/2.98 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(484,a,487,a)].
% 2.71/2.98 491 class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 2.71/2.98 492 class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add) # label(axiom). [assumption].
% 2.71/2.98 493 -class_OrderedGroup_Oordered__ab__group__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),B) != B | B = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_0) # label(axiom). [assumption].
% 2.71/2.98 494 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) # label(cls_less__eq__neg__nonpos_0) # label(axiom). [assumption].
% 2.71/2.98 495 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(B,hAPP(c_HOL_Ouminus__class_Ouminus(A),B),A) | -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_less__eq__neg__nonpos_1) # label(axiom). [assumption].
% 2.71/2.98 496 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) | -c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),B,A) # label(cls_neg__less__eq__nonneg_0) # label(axiom). [assumption].
% 2.78/3.05 497 -class_OrderedGroup_Oordered__ab__group__add(A) | c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(A),B),B,A) | -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_neg__less__eq__nonneg_1) # label(axiom). [assumption].
% 2.78/3.05 498 -class_OrderedGroup_Oordered__ab__group__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_neg__equal__zero_1) # label(axiom). [assumption].
% 2.78/3.05 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A) != A | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(492,a,493,a)].
% 2.78/3.05 499 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 2.78/3.05 500 -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].
% 2.78/3.05 501 -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].
% 2.78/3.05 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(499,a,500,a)].
% 2.78/3.05 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(499,a,501,a)].
% 2.78/3.05 502 class_Ring__and__Field_Opordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 2.78/3.05 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(502,a,500,a)].
% 2.78/3.05 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(502,a,501,a)].
% 2.78/3.05 503 class_OrderedGroup_Oab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 2.78/3.05 504 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__iff__diff__eq__0_0) # label(axiom). [assumption].
% 2.78/3.05 505 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) # label(cls_diff__def_0) # label(axiom). [assumption].
% 2.78/3.05 506 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) # label(cls_ab__diff__minus_0) # label(axiom). [assumption].
% 2.78/3.05 507 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D) | C = D # label(cls_eq__eqI_0) # label(axiom). [assumption].
% 2.78/3.05 508 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),D) | B = C # label(cls_eq__eqI_1) # label(axiom). [assumption].
% 2.78/3.05 509 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_ab__left__minus_0) # label(axiom). [assumption].
% 2.78/3.05 510 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_eq__iff__diff__eq__0_1) # label(axiom). [assumption].
% 2.78/3.05 511 -class_OrderedGroup_Oab__group__add(A) | c_Finite__Set_Osetsum(c_COMBB(c_HOL_Ouminus__class_Ouminus(A),B,A,A,C),D,C,A) = hAPP(c_HOL_Ouminus__class_Ouminus(A),c_Finite__Set_Osetsum(B,D,C,A)) # label(cls_setsum__negf_0) # label(axiom). [assumption].
% 2.78/3.05 512 -class_OrderedGroup_Oab__group__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),B) # label(cls_minus__diff__eq_0) # label(axiom). [assumption].
% 2.78/3.05 513 -class_OrderedGroup_Oab__group__add(A) | c_Finite__Set_Osetsum(c_COMBB(B,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),C,tc_nat,tc_nat,tc_nat),tc_nat,A,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),D,tc_nat),tc_nat,A) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),C),tc_nat),tc_nat,A)),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,A)) # label(cls_sumr__offset_0) # label(axiom). [assumption].
% 2.78/3.05 514 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)) # label(cls_Lim_Ominus__diff__minus_0) # label(axiom). [assumption].
% 2.78/3.05 515 -class_OrderedGroup_Oab__group__add(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) # label(cls_minus__add__distrib_0) # label(axiom). [assumption].
% 2.78/3.05 516 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B)) = C # label(cls_add__cancel__end_1) # label(axiom). [assumption].
% 2.78/3.05 517 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(A),B),D)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E)) # label(cls_Deriv_Oadd__diff__add_0) # label(axiom). [assumption].
% 2.78/3.05 518 -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 = hAPP(c_HOL_Ouminus__class_Ouminus(A),D) # label(cls_add__cancel__end_0) # label(axiom). [assumption].
% 2.78/3.05 519 -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].
% 2.78/3.05 520 -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].
% 2.78/3.05 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),A) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),C) | B = C. [resolve(503,a,507,a)].
% 2.78/3.05 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),C) | A = B. [resolve(503,a,508,a)].
% 2.78/3.05 Derived: c_Finite__Set_Osetsum(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A,tc_Int_Oint,tc_Int_Oint,B),C,B,tc_Int_Oint) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),c_Finite__Set_Osetsum(A,C,B,tc_Int_Oint)). [resolve(503,a,511,a)].
% 2.78/3.05 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),A). [resolve(503,a,512,a)].
% 2.78/3.05 Derived: c_Finite__Set_Osetsum(c_COMBB(A,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),B,tc_nat,tc_nat,tc_nat),tc_nat,tc_Int_Oint,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,tc_Int_Oint) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat),tc_nat,tc_Int_Oint)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat,tc_Int_Oint)). [resolve(503,a,513,a)].
% 2.78/3.05 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)). [resolve(503,a,514,a)].
% 2.78/3.05 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(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),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B)). [resolve(503,a,515,a)].
% 2.78/3.05 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),A)) = B. [resolve(503,a,516,a)].
% 2.78/3.05 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(tc_Int_Oint),A),C)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),D)). [resolve(503,a,517,a)].
% 2.78/3.05 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 = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),C). [resolve(503,a,518,a)].
% 2.78/3.05 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(503,a,519,a)].
% 2.78/3.05 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(503,a,520,a)].
% 2.78/3.05 521 class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 2.78/3.05 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),A) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),C) | B = C. [resolve(521,a,507,a)].
% 2.78/3.05 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C),C) | A = B. [resolve(521,a,508,a)].
% 2.78/3.05 Derived: c_Finite__Set_Osetsum(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,B),C,B,tc_Complex_Ocomplex) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_Finite__Set_Osetsum(A,C,B,tc_Complex_Ocomplex)). [resolve(521,a,511,a)].
% 2.78/3.05 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),A). [resolve(521,a,512,a)].
% 2.78/3.05 Derived: c_Finite__Set_Osetsum(c_COMBB(A,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),B,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat),tc_nat,tc_Complex_Ocomplex)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat,tc_Complex_Ocomplex)). [resolve(521,a,513,a)].
% 2.82/3.08 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)). [resolve(521,a,514,a)].
% 2.82/3.08 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(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),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)). [resolve(521,a,515,a)].
% 2.82/3.08 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),A)) = B. [resolve(521,a,516,a)].
% 2.82/3.08 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),D)). [resolve(521,a,517,a)].
% 2.82/3.08 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 = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),C). [resolve(521,a,518,a)].
% 2.82/3.08 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(521,a,519,a)].
% 2.82/3.08 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(521,a,520,a)].
% 2.82/3.08 522 class_Ring__and__Field_Oidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 2.82/3.08 523 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Osubr0__iff_1) # label(axiom). [assumption].
% 2.82/3.08 524 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_class__ringb_Osubr0__iff_0) # label(axiom). [assumption].
% 2.82/3.08 525 -class_Ring__and__Field_Oidom(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B) # label(cls_square__eq__iff_1) # label(axiom). [assumption].
% 2.82/3.08 526 -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 = hAPP(c_HOL_Ouminus__class_Ouminus(A),C) | B = C # label(cls_square__eq__iff_0) # label(axiom). [assumption].
% 2.82/3.08 527 -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].
% 2.82/3.08 528 -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].
% 2.82/3.08 529 -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].
% 2.82/3.08 530 -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].
% 2.82/3.08 531 -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].
% 2.82/3.08 532 -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].
% 2.82/3.08 533 -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].
% 2.82/3.08 534 -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].
% 2.82/3.08 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),A). [resolve(522,a,525,a)].
% 2.82/3.08 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 = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B) | A = B. [resolve(522,a,526,a)].
% 2.82/3.08 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(522,a,527,a)].
% 2.82/3.08 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(522,a,528,a)].
% 2.82/3.08 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(522,a,529,a)].
% 2.82/3.08 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(522,a,530,a)].
% 2.82/3.08 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(522,a,531,a)].
% 2.91/3.15 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),A),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),A),B)). [resolve(522,a,533,a)].
% 2.91/3.15 535 class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 2.91/3.15 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),A). [resolve(535,a,525,a)].
% 2.91/3.15 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 = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B) | A = B. [resolve(535,a,526,a)].
% 2.91/3.15 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(535,a,527,a)].
% 2.91/3.15 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(535,a,528,a)].
% 2.91/3.15 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(535,a,529,a)].
% 2.91/3.15 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(535,a,530,a)].
% 2.91/3.15 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(535,a,531,a)].
% 2.91/3.15 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),A),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)). [resolve(535,a,533,a)].
% 2.91/3.15 536 class_Ring__and__Field_Oabs__if(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oabs__if) # label(axiom). [assumption].
% 2.91/3.15 537 -class_Ring__and__Field_Oabs__if(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = hAPP(c_HOL_Ouminus__class_Ouminus(A),B) | -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if_0) # label(axiom). [assumption].
% 2.91/3.15 538 -class_Ring__and__Field_Oabs__if(A) | hAPP(c_HOL_Oabs__class_Oabs(A),B) = B | c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A) # label(cls_abs__if_1) # label(axiom). [assumption].
% 2.91/3.15 Derived: hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A) = A | c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(536,a,538,a)].
% 2.91/3.15 539 class_Ring__and__Field_Oordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 2.91/3.15 540 -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].
% 2.94/3.18 541 -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].
% 2.94/3.18 542 class_Ring__and__Field_Oordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 2.94/3.18 543 class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) # label(axiom). [assumption].
% 2.94/3.18 544 -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].
% 2.94/3.18 545 -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].
% 2.94/3.18 546 -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].
% 2.94/3.18 547 -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].
% 2.94/3.18 548 -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].
% 2.94/3.18 549 -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].
% 2.94/3.18 550 -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].
% 2.94/3.18 551 -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].
% 2.94/3.18 552 -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].
% 2.94/3.18 553 -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].
% 2.94/3.18 554 -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].
% 2.94/3.18 555 -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].
% 2.94/3.19 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(543,a,544,a)].
% 2.94/3.19 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(543,a,545,a)].
% 2.94/3.19 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(543,a,546,a)].
% 2.94/3.19 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(543,a,547,a)].
% 2.94/3.19 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(543,a,548,a)].
% 2.94/3.19 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(543,a,549,a)].
% 2.94/3.19 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(543,a,550,a)].
% 2.94/3.19 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(543,a,551,a)].
% 2.94/3.19 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(543,a,552,a)].
% 2.94/3.19 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(543,a,553,a)].
% 2.94/3.19 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(543,a,554,a)].
% 2.94/3.19 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(543,a,555,a)].
% 2.94/3.19 556 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].
% 2.94/3.19 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(556,a,544,a)].
% 2.94/3.19 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(556,a,545,a)].
% 2.94/3.19 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(556,a,546,a)].
% 2.94/3.19 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(556,a,547,a)].
% 3.02/3.29 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(556,a,548,a)].
% 3.02/3.29 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(556,a,549,a)].
% 3.02/3.29 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(556,a,550,a)].
% 3.02/3.29 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(556,a,551,a)].
% 3.02/3.29 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(556,a,552,a)].
% 3.02/3.29 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(556,a,553,a)].
% 3.02/3.29 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(556,a,554,a)].
% 3.02/3.29 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(556,a,555,a)].
% 3.02/3.29 557 class_Ring__and__Field_Olordered__ring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Olordered__ring) # label(axiom). [assumption].
% 3.02/3.29 558 -class_Ring__and__Field_Olordered__ring(A) | c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Oabs__class_Oabs(A),B)),hAPP(c_HOL_Oabs__class_Oabs(A),C)),A) # label(cls_abs__le__mult_0) # label(axiom). [assumption].
% 3.02/3.29 Derived: c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(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),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),A)),hAPP(c_HOL_Oabs__class_Oabs(tc_Int_Oint),B)),tc_Int_Oint). [resolve(557,a,558,a)].
% 3.02/3.29 559 class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) # label(axiom). [assumption].
% 3.02/3.29 560 -class_Ring__and__Field_Ofield(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__minus__divide__right_0) # label(axiom). [assumption].
% 3.02/3.29 561 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__minus__divide__divide_0) # label(axiom). [assumption].
% 3.02/3.29 562 -class_Ring__and__Field_Ofield(A) | c_Finite__Set_Osetsum(hAPP(c_Power_Opower__class_Opower(A),B),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),c_HOL_Oone__class_Oone(A))),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),c_HOL_Oone__class_Oone(A))) | B = c_HOL_Oone__class_Oone(A) # label(cls_geometric__sum_0) # label(axiom). [assumption].
% 3.02/3.29 563 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_Int_Onumber__class_Onumber__of(c_Int_OMin,A)),B) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),B)) # label(cls_minus1__divide_0) # label(axiom). [assumption].
% 3.02/3.29 564 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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_Oinverse__class_Odivide(A),C),D) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__divide__mult__cancel__left_0) # label(axiom). [assumption].
% 3.02/3.29 565 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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_Oinverse__class_Odivide(A),B),D) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_mult__divide__mult__cancel__right_0) # label(axiom). [assumption].
% 3.02/3.29 566 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),C) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_3) # label(axiom). [assumption].
% 3.02/3.29 567 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | B = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq_3) # label(axiom). [assumption].
% 3.02/3.29 568 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B)),B) = C # label(cls_divide__eq__imp_0) # label(axiom). [assumption].
% 3.02/3.29 569 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | C = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B)),B) # label(cls_eq__divide__imp_0) # label(axiom). [assumption].
% 3.02/3.29 570 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ozero__class_Ozero(A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B)),B) # label(cls_eq__divide__eq_4) # label(axiom). [assumption].
% 3.02/3.29 571 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | B = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_0) # label(axiom). [assumption].
% 3.02/3.29 572 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),C) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq_0) # label(axiom). [assumption].
% 3.02/3.29 573 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),E) | 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].
% 3.02/3.29 574 -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) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),E) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),C) # label(cls_frac__eq__eq_1) # label(axiom). [assumption].
% 3.02/3.29 575 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_4) # label(axiom). [assumption].
% 3.02/3.29 576 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),E)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(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)) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_diff__frac__eq_0) # label(axiom). [assumption].
% 3.02/3.29 577 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OMin,A)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),B) # label(cls_divide__minus1_0) # label(axiom). [assumption].
% 3.02/3.29 578 -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) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),c_Int_Onumber__class_Onumber__of(B,A)) # label(cls_eq__divide__eq__number__of1_2) # label(axiom). [assumption].
% 3.02/3.29 579 -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) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),c_HOL_Ozero__class_Ozero(A)) # label(cls_eq__divide__eq__number__of_2) # label(axiom). [assumption].
% 3.02/3.29 580 -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) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),c_HOL_Ozero__class_Ozero(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].
% 3.02/3.29 581 -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) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),c_HOL_Ozero__class_Ozero(A)) = c_Int_Onumber__class_Onumber__of(B,A) # label(cls_divide__eq__eq__number__of_2) # label(axiom). [assumption].
% 3.02/3.29 582 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_HOL_Ozero__class_Ozero(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].
% 3.02/3.29 583 -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) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),c_Int_Onumber__class_Onumber__of(B,A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of1_1) # label(axiom). [assumption].
% 3.02/3.29 584 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),B) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self__if_1) # label(axiom). [assumption].
% 3.02/3.29 585 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),B) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self_0) # label(axiom). [assumption].
% 3.02/3.29 586 -class_Ring__and__Field_Ofield(A) | B = c_HOL_Ozero__class_Ozero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),B) = c_HOL_Oone__class_Oone(A) # label(cls_right__inverse__eq_1) # label(axiom). [assumption].
% 3.02/3.29 587 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C) != c_HOL_Oone__class_Oone(A) | C = c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_right__inverse__eq_0) # label(axiom). [assumption].
% 3.02/3.29 588 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),D) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_nonzero__power__divide_0) # label(axiom). [assumption].
% 3.02/3.29 589 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),D) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__frac__num_0) # label(axiom). [assumption].
% 3.02/3.29 590 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))),D) | D = c_HOL_Ozero__class_Ozero(A) # label(cls_add__num__frac_0) # label(axiom). [assumption].
% 3.02/3.29 591 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),E)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),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)) | E = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__frac__eq_0) # label(axiom). [assumption].
% 3.02/3.29 592 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | c_HOL_Ozero__class_Ozero(A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),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)) # label(cls_eq__divide__eq__number__of1_4) # label(axiom). [assumption].
% 3.02/3.29 593 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),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)) = 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].
% 3.02/3.29 594 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | B = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),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)) | 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].
% 3.02/3.29 595 -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) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D) | 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].
% 3.02/3.29 596 -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) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C)),C) # label(cls_eq__divide__eq__number__of_4) # label(axiom). [assumption].
% 3.02/3.29 597 -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) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C)),C) = c_Int_Onumber__class_Onumber__of(B,A) # label(cls_divide__eq__eq__number__of_4) # label(axiom). [assumption].
% 3.02/3.29 598 -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) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C)),C) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__divide__eq__number__of_3) # label(axiom). [assumption].
% 3.02/3.29 599 -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),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_Int_Onumber__class_Onumber__of(C,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].
% 3.02/3.29 600 -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),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_Int_Onumber__class_Onumber__of(C,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].
% 3.02/3.29 601 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C)),C) = 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].
% 3.02/3.29 602 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),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)) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq__number__of1_4) # label(axiom). [assumption].
% 3.02/3.29 603 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C) != 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].
% 3.02/3.29 604 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_Finite__Set_Osetsum(B,C,D,A)),E) = c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),D),E,D,A,A),C,D,A) # label(cls_setsum__divide__distrib_0) # label(axiom). [assumption].
% 3.02/3.29 605 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OPls,A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__Numeral0_0) # label(axiom). [assumption].
% 3.02/3.29 606 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | c_HOL_Ozero__class_Ozero(A) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_HOL_Ozero__class_Ozero(A)) # label(cls_eq__divide__eq_2) # label(axiom). [assumption].
% 3.02/3.29 607 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__self__if_0) # label(axiom). [assumption].
% 3.02/3.29 608 -class_Ring__and__Field_Ofield(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C) # label(cls_minus__divide__left_0) # label(axiom). [assumption].
% 3.02/3.29 609 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) # label(cls_minus__divide__right_0) # label(axiom). [assumption].
% 3.02/3.29 610 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)) # label(cls_diff__divide__distrib_0) # label(axiom). [assumption].
% 3.02/3.29 611 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C) # label(cls_minus__divide__divide_0) # label(axiom). [assumption].
% 3.02/3.29 612 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__zero__left_0) # label(axiom). [assumption].
% 3.02/3.29 613 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__eq__eq_1) # label(axiom). [assumption].
% 3.02/3.29 614 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide__zero_0) # label(axiom). [assumption].
% 3.02/3.29 615 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),A)) = B # label(cls_divide__numeral__1_0) # label(axiom). [assumption].
% 3.02/3.29 616 -class_Ring__and__Field_Ofield(A) | -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),A)) = B # label(cls_divide__Numeral1_0) # label(axiom). [assumption].
% 3.02/3.29 617 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),c_HOL_Oone__class_Oone(A)) = B # label(cls_divide__1_0) # label(axiom). [assumption].
% 3.02/3.29 618 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),E)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) # label(cls_mult__frac__frac_0) # label(axiom). [assumption].
% 3.02/3.29 619 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),D) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) # label(cls_power__divide_0) # label(axiom). [assumption].
% 3.02/3.29 620 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Oone__class_Oone(A)),B)),C) # label(cls_power__one__over_0) # label(axiom). [assumption].
% 3.02/3.29 621 -class_Ring__and__Field_Ofield(A) | -class_Ring__and__Field_Odivision__by__zero(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)),D) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),C) # label(cls_mult__frac__num_0) # label(axiom). [assumption].
% 3.02/3.29 622 -class_Ring__and__Field_Ofield(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)) # label(cls_add__divide__distrib_0) # label(axiom). [assumption].
% 3.02/3.29 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(559,a,560,a)].
% 3.02/3.29 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(559,a,561,a)].
% 3.02/3.29 Derived: c_Finite__Set_Osetsum(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat,tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))) | A = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex). [resolve(559,a,562,a)].
% 3.02/3.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex)),A) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A)). [resolve(559,a,563,a)].
% 3.02/3.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(559,a,564,a)].
% 3.02/3.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),C) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(559,a,565,a)].
% 3.02/3.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),B) = A | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(559,a,566,a)].
% 3.02/3.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | A = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(559,a,567,a)].
% 3.02/3.29 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A)),A) = B. [resolve(559,a,568,a)].
% 3.02/3.29 Derived: A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A)),A). [resolve(559,a,569,a)].
% 3.02/3.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A)),A). [resolve(559,a,570,a)].
% 3.02/3.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | A = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(559,a,571,a)].
% 3.02/3.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),B) = A | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(559,a,572,a)].
% 3.02/3.29 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),D) | 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(559,a,573,a)].
% 3.02/3.29 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) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),D) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),B). [resolve(559,a,574,a)].
% 3.02/3.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(559,a,575,a)].
% 3.02/3.29 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(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)) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(559,a,576,a)].
% 3.02/3.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Complex_Ocomplex)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A). [resolve(559,a,577,a)].
% 3.02/3.29 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) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)). [resolve(559,a,578,a)].
% 3.02/3.29 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) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(559,a,579,a)].
% 3.02/3.29 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) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(559,a,580,a)].
% 3.02/3.29 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) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex). [resolve(559,a,581,a)].
% 3.02/3.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(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(559,a,582,a)].
% 3.02/3.29 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) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(559,a,583,a)].
% 3.02/3.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),A) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(559,a,584,a)].
% 3.02/3.29 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),A) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | A = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(559,a,585,a)].
% 3.02/3.29 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | A = B. [resolve(559,a,587,a)].
% 3.02/3.29 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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)) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(559,a,588,a)].
% 3.02/3.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B))),B) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(559,a,589,a)].
% 3.02/3.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C))),C) | C = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(559,a,590,a)].
% 3.02/3.29 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),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)) | D = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) | B = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(559,a,591,a)].
% 3.02/3.29 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) != hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C) | 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(559,a,595,a)].
% 3.02/3.29 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) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)),B)),B). [resolve(559,a,596,a)].
% 3.02/3.29 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) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)),B)),B) = c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex). [resolve(559,a,597,a)].
% 3.02/3.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B) != 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(559,a,603,a)].
% 3.02/3.29 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_Finite__Set_Osetsum(A,B,C,tc_Complex_Ocomplex)),D) = c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),C),D,C,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B,C,tc_Complex_Ocomplex). [resolve(559,a,604,a)].
% 3.02/3.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(559,a,605,a)].
% 3.02/3.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)). [resolve(559,a,606,a)].
% 3.02/3.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(559,a,607,a)].
% 3.02/3.29 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),B). [resolve(559,a,608,a)].
% 3.02/3.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)). [resolve(559,a,609,a)].
% 3.02/3.29 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C)). [resolve(559,a,610,a)].
% 3.02/3.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B). [resolve(559,a,611,a)].
% 3.02/3.29 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(559,a,612,a)].
% 3.02/3.29 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex). [resolve(559,a,613,a)].
% 3.09/3.33 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_Complex_Ocomplex)) = A. [resolve(559,a,615,a)].
% 3.09/3.33 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(559,a,617,a)].
% 3.09/3.33 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),D)) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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(559,a,618,a)].
% 3.09/3.33 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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(559,a,619,a)].
% 3.09/3.33 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(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),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A)),B). [resolve(559,a,620,a)].
% 3.09/3.33 Derived: -class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C)),B). [resolve(559,a,621,a)].
% 3.09/3.33 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(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_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),C)). [resolve(559,a,622,a)].
% 3.09/3.33 623 class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) # label(axiom). [assumption].
% 3.09/3.33 624 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(c_COMBB(c_HOL_Ouminus__class_Ouminus(A),B,A,A,A),C,A) | -c_Deriv_Odifferentiable(B,C,A) # label(cls_differentiable__minus_0) # label(axiom). [assumption].
% 3.09/3.33 625 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(c_COMBB(B,C,A,A,A),D,A) | -c_Deriv_Odifferentiable(C,D,A) | -c_Deriv_Odifferentiable(B,hAPP(C,D),A) # label(cls_differentiable__compose_0) # label(axiom). [assumption].
% 3.09/3.33 626 -class_RealVector_Oreal__normed__field(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),C,A,tc_fun(A,A),B),D,B,A,A),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(C,E,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_divide_OLIM__zero_0) # label(axiom). [assumption].
% 3.09/3.33 627 -class_RealVector_Oreal__normed__field(A) | c_Lim_OLIM(c_COMBC(c_HOL_Oinverse__class_Odivide(A),B,A,A,A),C,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),B),A,A) # label(cls_divide_Ocont_0) # label(axiom). [assumption].
% 3.09/3.33 628 -class_RealVector_Oreal__normed__field(A) | c_Lim_OisCont(c_COMBC(c_HOL_Oinverse__class_Odivide(A),B,A,A,A),C,A,A) # label(cls_divide_OisCont_0) # label(axiom). [assumption].
% 3.09/3.33 629 -class_RealVector_Oreal__normed__field(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),C,A,tc_fun(A,A),B),D,B,A,A),E,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),F),D),B,A) | -c_Lim_OLIM(C,E,F,B,A) # label(cls_divide_OLIM_0) # label(axiom). [assumption].
% 3.09/3.33 630 -class_RealVector_Oreal__normed__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_Finite__Set_Osetsum(B,C,D,A)),E) = c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),D),E,D,A,A),C,D,A) # label(cls_divide_Osetsum_0) # label(axiom). [assumption].
% 3.09/3.33 631 -class_RealVector_Oreal__normed__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)) # label(cls_divide_Odiff_0) # label(axiom). [assumption].
% 3.09/3.33 632 -class_RealVector_Oreal__normed__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),C)) # label(cls_divide_Ominus_0) # label(axiom). [assumption].
% 3.09/3.33 633 -class_RealVector_Oreal__normed__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_divide_Ozero_0) # label(axiom). [assumption].
% 3.09/3.33 634 -class_RealVector_Oreal__normed__field(A) | c_Series_Osums(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),C),A) | -c_Series_Osums(B,D,A) # label(cls_sums__divide_0) # label(axiom). [assumption].
% 3.09/3.33 635 -class_RealVector_Oreal__normed__field(A) | c_Series_Osums(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),C),A) | -c_Series_Osums(B,D,A) # label(cls_divide_Osums_0) # label(axiom). [assumption].
% 3.09/3.33 636 -class_RealVector_Oreal__normed__field(A) | c_SEQ_OCauchy(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),A) | -c_SEQ_OCauchy(B,A) # label(cls_divide_OCauchy_0) # label(axiom). [assumption].
% 3.09/3.33 637 -class_RealVector_Oreal__normed__field(A) | c_SEQ_OZseq(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),A) | -c_SEQ_OZseq(B,A) # label(cls_divide_OZseq_0) # label(axiom). [assumption].
% 3.09/3.33 638 -class_RealVector_Oreal__normed__field(A) | c_SEQ_OLIMSEQ(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),D),C),A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_divide_OLIMSEQ_0) # label(axiom). [assumption].
% 3.09/3.33 639 -class_RealVector_Oreal__normed__field(A) | c_Series_Osummable(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),A) | -c_Series_Osummable(B,A) # label(cls_summable__divide_0) # label(axiom). [assumption].
% 3.09/3.33 640 -class_RealVector_Oreal__normed__field(A) | c_Series_Osummable(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),A) | -c_Series_Osummable(B,A) # label(cls_divide_Osummable_0) # label(axiom). [assumption].
% 3.09/3.33 641 -class_RealVector_Oreal__normed__field(A) | c_Deriv_Odifferentiable(c_COMBC(c_COMBB(c_Power_Opower__class_Opower(A),B,A,tc_fun(tc_nat,A),A),C,A,tc_nat,A),D,A) | -c_Deriv_Odifferentiable(B,D,A) # label(cls_differentiable__power_0) # label(axiom). [assumption].
% 3.09/3.33 642 -class_RealVector_Oreal__normed__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),B),D)),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),C),D)) # label(cls_divide_Oadd_0) # label(axiom). [assumption].
% 3.09/3.33 Derived: c_Deriv_Odifferentiable(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,B,tc_Complex_Ocomplex). [resolve(623,a,624,a)].
% 3.09/3.33 Derived: c_Deriv_Odifferentiable(c_COMBB(A,B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(B,C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,hAPP(B,C),tc_Complex_Ocomplex). [resolve(623,a,625,a)].
% 3.09/3.36 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(623,a,626,a)].
% 3.09/3.36 Derived: c_Lim_OLIM(c_COMBC(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B),A),tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(623,a,627,a)].
% 3.09/3.36 Derived: c_Lim_OisCont(c_COMBC(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(623,a,628,a)].
% 3.09/3.36 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D,hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),E),C),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,E,A,tc_Complex_Ocomplex). [resolve(623,a,629,a)].
% 3.09/3.36 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),B) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A),B)). [resolve(623,a,632,a)].
% 3.09/3.36 Derived: c_Series_Osums(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_Series_Osums(A,C,tc_Complex_Ocomplex). [resolve(623,a,634,a)].
% 3.09/3.36 Derived: c_SEQ_OCauchy(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_SEQ_OCauchy(A,tc_Complex_Ocomplex). [resolve(623,a,636,a)].
% 3.09/3.36 Derived: c_SEQ_OZseq(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_SEQ_OZseq(A,tc_Complex_Ocomplex). [resolve(623,a,637,a)].
% 3.09/3.36 Derived: c_SEQ_OLIMSEQ(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(623,a,638,a)].
% 3.09/3.36 Derived: c_Series_Osummable(c_COMBC(c_COMBB(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(623,a,639,a)].
% 3.09/3.36 Derived: c_Deriv_Odifferentiable(c_COMBC(c_COMBB(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_nat,tc_Complex_Ocomplex),C,tc_Complex_Ocomplex) | -c_Deriv_Odifferentiable(A,C,tc_Complex_Ocomplex). [resolve(623,a,641,a)].
% 3.09/3.36 643 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 3.09/3.36 644 -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].
% 3.14/3.42 645 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].
% 3.14/3.42 646 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.14/3.42 647 -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].
% 3.14/3.42 648 -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].
% 3.14/3.42 649 -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].
% 3.14/3.42 650 -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].
% 3.14/3.42 651 -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].
% 3.14/3.42 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(646,a,647,a)].
% 3.14/3.42 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(646,a,648,a)].
% 3.14/3.42 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(646,a,651,a)].
% 3.14/3.42 652 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.14/3.42 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(652,a,647,a)].
% 3.14/3.42 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(652,a,648,a)].
% 3.14/3.42 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(652,a,651,a)].
% 3.14/3.42 653 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) # label(axiom). [assumption].
% 3.14/3.42 654 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),C),D,A,A,B),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(D,E,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_LIM__mult__right__zero_0) # label(axiom). [assumption].
% 3.14/3.42 655 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),C),D,A,A,B),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(D,E,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__right_OLIM__zero_0) # label(axiom). [assumption].
% 3.14/3.42 656 -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].
% 3.14/3.42 657 -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].
% 3.14/3.42 658 -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].
% 3.14/3.42 659 -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].
% 3.14/3.42 660 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) # label(cls_mult__right_Ominus_0) # label(axiom). [assumption].
% 3.14/3.42 661 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) # label(cls_mult_Ominus__right_0) # label(axiom). [assumption].
% 3.14/3.42 662 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) # label(cls_mult__left_Ominus_0) # label(axiom). [assumption].
% 3.14/3.42 663 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) # label(cls_mult_Ominus__left_0) # label(axiom). [assumption].
% 3.14/3.42 664 -class_RealVector_Oreal__normed__algebra(A) | c_Lim_OLIM(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A,A) # label(cls_mult__right_Ocont_0) # label(axiom). [assumption].
% 3.14/3.42 665 -class_RealVector_Oreal__normed__algebra(A) | c_Lim_OisCont(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A) # label(cls_mult__right_OisCont_0) # label(axiom). [assumption].
% 3.14/3.42 666 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_Odiff_0) # label(axiom). [assumption].
% 3.14/3.42 667 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_mult_Odiff__right_0) # label(axiom). [assumption].
% 3.14/3.42 668 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_mult_Odiff__left_0) # label(axiom). [assumption].
% 3.14/3.42 669 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_Odiff_0) # label(axiom). [assumption].
% 3.14/3.42 670 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),C),D,A,A,B),E,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),F),B,A) | -c_Lim_OLIM(D,E,F,B,A) # label(cls_mult__right_OLIM_0) # label(axiom). [assumption].
% 3.14/3.42 671 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Finite__Set_Osetsum(C,D,E,A)) = c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A,E),D,E,A) # label(cls_mult__right_Osetsum_0) # label(axiom). [assumption].
% 3.14/3.42 672 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D)),E))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E))) # label(cls_mult_Oprod__diff__prod_0) # label(axiom). [assumption].
% 3.14/3.42 673 -class_RealVector_Oreal__normed__algebra(A) | c_Lim_OisCont(c_COMBC(c_HOL_Otimes__class_Otimes(A),B,A,A,A),C,A,A) # label(cls_mult__left_OisCont_0) # label(axiom). [assumption].
% 3.14/3.42 674 -class_RealVector_Oreal__normed__algebra(A) | c_Lim_OLIM(c_COMBC(c_HOL_Otimes__class_Otimes(A),B,A,A,A),C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),A,A) # label(cls_mult__left_Ocont_0) # label(axiom). [assumption].
% 3.14/3.42 675 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OCauchy(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A,tc_nat),A) | -c_SEQ_OCauchy(C,A) # label(cls_mult__right_OCauchy_0) # label(axiom). [assumption].
% 3.14/3.42 676 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OLIMSEQ(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_SEQ_OLIMSEQ(C,D,A) # label(cls_mult__right_OLIMSEQ_0) # label(axiom). [assumption].
% 3.14/3.42 677 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OZseq(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A,tc_nat),A) | -c_SEQ_OZseq(C,A) # label(cls_mult__right_OZseq_0) # label(axiom). [assumption].
% 3.14/3.42 678 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OZseq(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A,tc_nat),A) | -c_SEQ_OZseq(C,A) # label(cls_Zseq__mult__right_0) # label(axiom). [assumption].
% 3.14/3.42 679 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osummable(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A,tc_nat),A) | -c_Series_Osummable(C,A) # label(cls_summable__mult_0) # label(axiom). [assumption].
% 3.14/3.42 680 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osummable(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A,tc_nat),A) | -c_Series_Osummable(C,A) # label(cls_mult__right_Osummable_0) # label(axiom). [assumption].
% 3.14/3.42 681 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osums(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_Series_Osums(C,D,A) # label(cls_mult__right_Osums_0) # label(axiom). [assumption].
% 3.14/3.42 682 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osums(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),C,A,A,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) | -c_Series_Osums(C,D,A) # label(cls_sums__mult_0) # label(axiom). [assumption].
% 3.14/3.42 683 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),C,A,tc_fun(A,A),B),D,B,A,A),E,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),F),D),B,A) | -c_Lim_OLIM(C,E,F,B,A) # label(cls_mult__left_OLIM_0) # label(axiom). [assumption].
% 3.14/3.42 684 -class_RealVector_Oreal__normed__algebra(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Finite__Set_Osetsum(B,C,D,A)),E) = c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),D),E,D,A,A),C,D,A) # label(cls_mult__left_Osetsum_0) # label(axiom). [assumption].
% 3.14/3.42 685 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),C,A,tc_fun(A,A),B),D,B,A,A),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(C,E,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_LIM__mult__left__zero_0) # label(axiom). [assumption].
% 3.14/3.42 686 -class_RealVector_Oreal__normed__algebra(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),C,A,tc_fun(A,A),B),D,B,A,A),E,c_HOL_Ozero__class_Ozero(A),B,A) | -c_Lim_OLIM(C,E,c_HOL_Ozero__class_Ozero(A),B,A) # label(cls_mult__left_OLIM__zero_0) # label(axiom). [assumption].
% 3.14/3.42 687 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OZseq(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),A) | -c_SEQ_OZseq(B,A) # label(cls_mult__left_OZseq_0) # label(axiom). [assumption].
% 3.14/3.42 688 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OZseq(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),A) | -c_SEQ_OZseq(B,A) # label(cls_Zseq__mult__left_0) # label(axiom). [assumption].
% 3.14/3.42 689 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OLIMSEQ(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_mult__left_OLIMSEQ_0) # label(axiom). [assumption].
% 3.14/3.42 690 -class_RealVector_Oreal__normed__algebra(A) | c_SEQ_OCauchy(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),A) | -c_SEQ_OCauchy(B,A) # label(cls_mult__left_OCauchy_0) # label(axiom). [assumption].
% 3.14/3.42 691 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osummable(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),A) | -c_Series_Osummable(B,A) # label(cls_mult__left_Osummable_0) # label(axiom). [assumption].
% 3.14/3.42 692 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osummable(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),A) | -c_Series_Osummable(B,A) # label(cls_summable__mult2_0) # label(axiom). [assumption].
% 3.14/3.42 693 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osums(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_Series_Osums(B,D,A) # label(cls_mult__left_Osums_0) # label(axiom). [assumption].
% 3.14/3.42 694 -class_RealVector_Oreal__normed__algebra(A) | c_Series_Osums(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(A),B,A,tc_fun(A,A),tc_nat),C,tc_nat,A,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) | -c_Series_Osums(B,D,A) # label(cls_sums__mult2_0) # label(axiom). [assumption].
% 3.14/3.42 695 -class_RealVector_Ometric__space(A) | -class_RealVector_Oreal__normed__algebra(B) | -class_Power_Opower(B) | c_Lim_OisCont(c_COMBC(c_COMBB(c_Power_Opower__class_Opower(B),C,B,tc_fun(tc_nat,B),A),D,A,tc_nat,B),E,A,B) | -c_Lim_OisCont(C,E,A,B) # label(cls_isCont__power_0) # label(axiom). [assumption].
% 3.14/3.42 696 -class_RealVector_Oreal__normed__algebra(A) | -class_Power_Opower(A) | -class_RealVector_Ometric__space(B) | c_Lim_OLIM(c_COMBC(c_COMBB(c_Power_Opower__class_Opower(A),C,A,tc_fun(tc_nat,A),B),D,B,tc_nat,A),E,hAPP(hAPP(c_Power_Opower__class_Opower(A),F),D),B,A) | -c_Lim_OLIM(C,E,F,B,A) # label(cls_LIM__power_0) # label(axiom). [assumption].
% 3.14/3.42 697 -class_RealVector_Oreal__normed__algebra(A) | -class_Power_Opower(A) | c_SEQ_OLIMSEQ(c_COMBC(c_COMBB(c_Power_Opower__class_Opower(A),B,A,tc_fun(tc_nat,A),tc_nat),C,tc_nat,tc_nat,A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A) | -c_SEQ_OLIMSEQ(B,D,A) # label(cls_LIMSEQ__pow_0) # label(axiom). [assumption].
% 3.14/3.42 698 -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].
% 3.14/3.42 699 -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].
% 3.14/3.42 700 -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].
% 3.14/3.42 701 -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].
% 3.14/3.42 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C,tc_Complex_Ocomplex,tc_Complex_Ocomplex,A),D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(C,D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(653,a,654,a)].
% 3.14/3.42 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(653,a,656,a)].
% 3.14/3.42 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(653,a,658,a)].
% 3.14/3.42 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)). [resolve(653,a,660,a)].
% 3.14/3.42 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),B) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B)). [resolve(653,a,662,a)].
% 3.14/3.42 Derived: c_Lim_OLIM(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B),tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(653,a,664,a)].
% 3.14/3.42 Derived: c_Lim_OisCont(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(653,a,665,a)].
% 3.14/3.42 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(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(653,a,666,a)].
% 3.14/3.42 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),B)),C) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(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(653,a,668,a)].
% 3.14/3.42 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),C,tc_Complex_Ocomplex,tc_Complex_Ocomplex,A),D,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),E),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(C,D,E,A,tc_Complex_Ocomplex). [resolve(653,a,670,a)].
% 3.14/3.42 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(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_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),D))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C)),D))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),D))). [resolve(653,a,672,a)].
% 3.14/3.43 Derived: c_Lim_OisCont(c_COMBC(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(653,a,673,a)].
% 3.14/3.43 Derived: c_Lim_OLIM(c_COMBC(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_Complex_Ocomplex),B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B),A),tc_Complex_Ocomplex,tc_Complex_Ocomplex). [resolve(653,a,674,a)].
% 3.14/3.43 Derived: c_SEQ_OCauchy(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) | -c_SEQ_OCauchy(B,tc_Complex_Ocomplex). [resolve(653,a,675,a)].
% 3.14/3.43 Derived: c_SEQ_OLIMSEQ(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(B,C,tc_Complex_Ocomplex). [resolve(653,a,676,a)].
% 3.14/3.43 Derived: c_SEQ_OZseq(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) | -c_SEQ_OZseq(B,tc_Complex_Ocomplex). [resolve(653,a,677,a)].
% 3.14/3.43 Derived: c_Series_Osummable(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) | -c_Series_Osummable(B,tc_Complex_Ocomplex). [resolve(653,a,679,a)].
% 3.14/3.43 Derived: c_Series_Osums(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),C),tc_Complex_Ocomplex) | -c_Series_Osums(B,C,tc_Complex_Ocomplex). [resolve(653,a,681,a)].
% 3.14/3.43 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),E),C),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,E,A,tc_Complex_Ocomplex). [resolve(653,a,683,a)].
% 3.14/3.43 Derived: -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),A),C,A,tc_Complex_Ocomplex,tc_Complex_Ocomplex),D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex). [resolve(653,a,685,a)].
% 3.14/3.43 Derived: c_SEQ_OZseq(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_SEQ_OZseq(A,tc_Complex_Ocomplex). [resolve(653,a,687,a)].
% 3.14/3.43 Derived: c_SEQ_OLIMSEQ(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(653,a,689,a)].
% 3.14/3.43 Derived: c_SEQ_OCauchy(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_SEQ_OCauchy(A,tc_Complex_Ocomplex). [resolve(653,a,690,a)].
% 3.14/3.43 Derived: c_Series_Osummable(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_Complex_Ocomplex) | -c_Series_Osummable(A,tc_Complex_Ocomplex). [resolve(653,a,691,a)].
% 3.20/3.46 Derived: c_Series_Osums(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_Complex_Ocomplex,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_Complex_Ocomplex,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_Series_Osums(A,C,tc_Complex_Ocomplex). [resolve(653,a,693,a)].
% 3.20/3.46 Derived: -class_RealVector_Ometric__space(A) | -class_Power_Opower(tc_Complex_Ocomplex) | c_Lim_OisCont(c_COMBC(c_COMBB(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),A),C,A,tc_nat,tc_Complex_Ocomplex),D,A,tc_Complex_Ocomplex) | -c_Lim_OisCont(B,D,A,tc_Complex_Ocomplex). [resolve(653,a,695,b)].
% 3.20/3.46 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | -class_RealVector_Ometric__space(A) | c_Lim_OLIM(c_COMBC(c_COMBB(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B,tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),A),C,A,tc_nat,tc_Complex_Ocomplex),D,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),E),C),A,tc_Complex_Ocomplex) | -c_Lim_OLIM(B,D,E,A,tc_Complex_Ocomplex). [resolve(653,a,696,a)].
% 3.20/3.46 Derived: -class_Power_Opower(tc_Complex_Ocomplex) | c_SEQ_OLIMSEQ(c_COMBC(c_COMBB(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A,tc_Complex_Ocomplex,tc_fun(tc_nat,tc_Complex_Ocomplex),tc_nat),B,tc_nat,tc_nat,tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),C),B),tc_Complex_Ocomplex) | -c_SEQ_OLIMSEQ(A,C,tc_Complex_Ocomplex). [resolve(653,a,697,a)].
% 3.20/3.46 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(653,a,698,a)].
% 3.20/3.46 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(653,a,700,a)].
% 3.20/3.46 702 class_Ring__and__Field_Oring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring) # label(axiom). [assumption].
% 3.20/3.46 703 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) # label(cls_minus__mult__commute_0) # label(axiom). [assumption].
% 3.20/3.46 704 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) # label(cls_minus__mult__minus_0) # label(axiom). [assumption].
% 3.20/3.46 705 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_HOL_Ouminus__class_Ouminus(A),C)) # label(cls_minus__mult__right_0) # label(axiom). [assumption].
% 3.20/3.46 706 -class_Ring__and__Field_Oring(A) | hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C) # label(cls_minus__mult__left_0) # label(axiom). [assumption].
% 3.20/3.46 707 -class_Ring__and__Field_Oring(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),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),D),B)),C)),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)),E) # label(cls_eq__add__iff2_1) # label(axiom). [assumption].
% 3.20/3.46 708 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C)),D)) # label(cls_eq__add__iff1_1) # label(axiom). [assumption].
% 3.20/3.46 709 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),E)),C)),D) = F # label(cls_eq__add__iff1_0) # label(axiom). [assumption].
% 3.20/3.46 710 -class_Ring__and__Field_Oring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F) | D = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B)),C)),F) # label(cls_eq__add__iff2_0) # label(axiom). [assumption].
% 3.20/3.46 711 -class_Ring__and__Field_Oring(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_Ominus__class_Ominus(A),C),D)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(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__diff__distrib__number__of_0) # label(axiom). [assumption].
% 3.20/3.46 712 -class_Ring__and__Field_Oring(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),c_Int_Onumber__class_Onumber__of(D,A)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(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__diff__distrib__number__of_0) # label(axiom). [assumption].
% 3.20/3.46 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B)). [resolve(702,a,703,a)].
% 3.20/3.46 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B). [resolve(702,a,704,a)].
% 3.20/3.46 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(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),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),B)). [resolve(702,a,705,a)].
% 3.20/3.46 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(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),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),B). [resolve(702,a,706,a)].
% 3.20/3.46 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),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),C),A)),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B)),D). [resolve(702,a,707,a)].
% 3.20/3.46 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(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),D),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C)). [resolve(702,a,708,a)].
% 3.20/3.46 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(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),D),B)),E) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),D)),B)),C) = E. [resolve(702,a,709,a)].
% 3.20/3.46 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(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),D),B)),E) | C = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),D),A)),B)),E). [resolve(702,a,710,a)].
% 3.20/3.46 Derived: -class_Int_Onumber(tc_Int_Oint) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),B),C)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)),C)). [resolve(702,a,711,a)].
% 3.20/3.46 Derived: -class_Int_Onumber(tc_Int_Oint) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint))). [resolve(702,a,712,a)].
% 3.20/3.46 713 class_Ring__and__Field_Oring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring) # label(axiom). [assumption].
% 3.20/3.46 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)). [resolve(713,a,703,a)].
% 3.20/3.46 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),B). [resolve(713,a,704,a)].
% 3.20/3.46 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(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),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),B)). [resolve(713,a,705,a)].
% 3.20/3.46 Derived: hAPP(c_HOL_Ouminus__class_Ouminus(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),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),B). [resolve(713,a,706,a)].
% 3.20/3.46 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),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),C),A)),B)),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),C),B)),D). [resolve(713,a,707,a)].
% 3.20/3.46 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(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),D),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),D)),B)),C)). [resolve(713,a,708,a)].
% 3.20/3.46 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(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),D),B)),E) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),D)),B)),C) = E. [resolve(713,a,709,a)].
% 3.23/3.52 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(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),D),B)),E) | C = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),D),A)),B)),E). [resolve(713,a,710,a)].
% 3.23/3.52 714 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].
% 3.23/3.52 715 -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].
% 3.23/3.52 716 -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].
% 3.23/3.52 717 -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].
% 3.23/3.52 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(714,a,715,a)].
% 3.23/3.52 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(714,a,716,a)].
% 3.23/3.52 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(714,a,717,a)].
% 3.23/3.52 718 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].
% 3.23/3.52 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(718,a,717,a)].
% 3.23/3.52 719 class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1) # label(axiom). [assumption].
% 3.23/3.52 720 -class_Ring__and__Field_Ocomm__ring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_neg__power__if_0) # label(axiom). [assumption].
% 3.23/3.52 721 -class_Ring__and__Field_Ocomm__ring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C) = hAPP(c_HOL_Ouminus__class_Ouminus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_neg__power__if_1) # label(axiom). [assumption].
% 3.23/3.52 722 -class_Ring__and__Field_Ocomm__ring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oone__class_Oone(A))),B) = hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oone__class_Oone(A)) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) # label(cls_minus__one__odd__power_0) # label(axiom). [assumption].
% 3.23/3.52 723 -class_Ring__and__Field_Ocomm__ring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oone__class_Oone(A))),B) = c_HOL_Oone__class_Oone(A) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) # label(cls_minus__one__even__power_0) # label(axiom). [assumption].
% 3.23/3.52 724 -class_Ring__and__Field_Ocomm__ring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oone__class_Oone(A))),hAPP(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(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oone__class_Oone(A)) # label(cls_power__minus1__odd_0) # label(axiom). [assumption].
% 3.23/3.52 725 -class_Ring__and__Field_Ocomm__ring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Ouminus__class_Ouminus(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),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].
% 3.23/3.52 726 -class_Ring__and__Field_Ocomm__ring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Ouminus__class_Ouminus(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),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].
% 3.23/3.52 727 -class_Ring__and__Field_Ocomm__ring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oone__class_Oone(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].
% 3.23/3.52 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),B) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(719,a,720,a)].
% 3.23/3.52 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),B) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(719,a,721,a)].
% 3.23/3.52 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))),A) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)) | c_Parity_Oeven__odd__class_Oeven(A,tc_nat). [resolve(719,a,722,a)].
% 3.23/3.52 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))),A) = c_HOL_Oone__class_Oone(tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(A,tc_nat). [resolve(719,a,723,a)].
% 3.23/3.52 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))),hAPP(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))) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)). [resolve(719,a,724,a)].
% 3.23/3.52 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(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),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(719,a,725,a)].
% 3.23/3.52 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(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),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(719,a,726,a)].
% 3.23/3.52 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),c_HOL_Oone__class_Oone(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(719,a,727,a)].
% 3.28/3.55 728 class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) # label(axiom). [assumption].
% 3.28/3.55 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),B) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(728,a,720,a)].
% 3.28/3.55 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),B) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(728,a,721,a)].
% 3.28/3.55 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),A) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) | c_Parity_Oeven__odd__class_Oeven(A,tc_nat). [resolve(728,a,722,a)].
% 3.28/3.55 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),A) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) | -c_Parity_Oeven__odd__class_Oeven(A,tc_nat). [resolve(728,a,723,a)].
% 3.28/3.55 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),hAPP(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))) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)). [resolve(728,a,724,a)].
% 3.28/3.55 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),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_Complex_Ocomplex),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(728,a,725,a)].
% 3.28/3.55 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(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),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(728,a,726,a)].
% 3.28/3.55 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(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(728,a,727,a)].
% 3.28/3.55 729 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 3.28/3.55 730 -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].
% 3.28/3.55 731 -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].
% 3.28/3.55 732 -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].
% 3.28/3.55 733 -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].
% 3.28/3.55 734 -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].
% 3.28/3.55 735 -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].
% 3.28/3.55 736 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(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].
% 3.28/3.55 737 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(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].
% 3.28/3.55 738 -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),hAPP(c_Suc,C)) # label(cls_class__semiring_Osemiring__rules_I27_J_0) # label(axiom). [assumption].
% 3.28/3.55 739 -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),hAPP(c_Suc,C)) # label(cls_class__semiring_Osemiring__rules_I28_J_0) # label(axiom). [assumption].
% 3.28/3.55 740 -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].
% 3.28/3.55 741 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(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].
% 3.28/3.55 742 -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].
% 3.28/3.55 743 -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].
% 3.28/3.55 744 -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].
% 3.28/3.55 745 -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].
% 3.28/3.55 746 -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].
% 3.28/3.55 747 -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].
% 3.28/3.55 748 -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].
% 3.28/3.55 749 -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].
% 3.28/3.55 750 -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].
% 3.28/3.55 751 -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].
% 3.28/3.55 752 -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].
% 3.28/3.55 753 -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].
% 3.28/3.55 754 -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].
% 3.28/3.55 755 -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].
% 3.28/3.55 756 -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].
% 3.28/3.55 757 -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].
% 3.28/3.55 758 -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].
% 3.28/3.55 759 -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].
% 3.28/3.55 760 -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].
% 3.28/3.55 761 -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].
% 3.28/3.55 762 -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].
% 3.28/3.55 763 -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].
% 3.28/3.55 764 -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].
% 3.28/3.55 765 -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].
% 3.28/3.55 766 -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].
% 3.28/3.55 767 -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].
% 3.28/3.55 768 -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].
% 3.28/3.55 769 -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].
% 3.28/3.55 770 -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].
% 3.28/3.55 771 -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].
% 3.28/3.55 772 -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].
% 3.28/3.55 773 -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].
% 3.28/3.55 774 -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].
% 3.31/3.55 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(729,a,730,a)].
% 3.31/3.55 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(729,a,731,a)].
% 3.31/3.55 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(729,a,733,a)].
% 3.31/3.55 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(729,a,734,a)].
% 3.31/3.55 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(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(729,a,736,a)].
% 3.31/3.55 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),hAPP(c_Suc,B)). [resolve(729,a,738,a)].
% 3.31/3.55 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),hAPP(c_Suc,B)). [resolve(729,a,739,a)].
% 3.31/3.55 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(729,a,740,a)].
% 3.31/3.55 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(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(729,a,741,a)].
% 3.31/3.55 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(729,a,742,a)].
% 3.31/3.55 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(729,a,744,a)].
% 3.31/3.55 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(729,a,745,a)].
% 3.31/3.55 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(729,a,746,a)].
% 3.31/3.55 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(729,a,747,a)].
% 3.31/3.55 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(729,a,748,a)].
% 3.31/3.55 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(729,a,749,a)].
% 3.31/3.55 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(729,a,750,a)].
% 3.31/3.55 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(729,a,751,a)].
% 3.31/3.55 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(729,a,752,a)].
% 3.31/3.55 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(729,a,753,a)].
% 3.31/3.55 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(729,a,754,a)].
% 3.31/3.55 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(729,a,756,a)].
% 3.31/3.55 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(729,a,757,a)].
% 3.31/3.55 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(729,a,758,a)].
% 3.31/3.55 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(729,a,761,a)].
% 3.31/3.55 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(729,a,762,a)].
% 3.31/3.55 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = A. [resolve(729,a,763,a)].
% 3.31/3.55 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(729,a,764,a)].
% 3.31/3.55 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(729,a,766,a)].
% 3.31/3.55 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(729,a,767,a)].
% 3.31/3.55 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(729,a,769,a)].
% 3.31/3.55 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(729,a,771,a)].
% 3.31/3.55 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(729,a,772,a)].
% 3.31/3.55 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(729,a,773,a)].
% 3.31/3.55 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(729,a,774,a)].
% 3.31/3.56 775 class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 3.31/3.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A) = A. [resolve(775,a,733,a)].
% 3.31/3.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(775,a,734,a)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(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(775,a,736,a)].
% 3.31/3.56 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),hAPP(c_Suc,B)). [resolve(775,a,738,a)].
% 3.31/3.56 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),hAPP(c_Suc,B)). [resolve(775,a,739,a)].
% 3.31/3.56 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(775,a,740,a)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(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(775,a,741,a)].
% 3.31/3.56 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(775,a,742,a)].
% 3.31/3.56 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(775,a,744,a)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(775,a,745,a)].
% 3.31/3.56 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(775,a,746,a)].
% 3.31/3.56 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(775,a,747,a)].
% 3.31/3.56 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(775,a,748,a)].
% 3.31/3.56 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(775,a,749,a)].
% 3.31/3.56 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(775,a,750,a)].
% 3.31/3.56 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(775,a,751,a)].
% 3.31/3.56 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(775,a,752,a)].
% 3.31/3.56 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(775,a,753,a)].
% 3.31/3.56 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(775,a,754,a)].
% 3.31/3.56 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(775,a,756,a)].
% 3.31/3.56 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(775,a,757,a)].
% 3.31/3.56 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(775,a,758,a)].
% 3.31/3.56 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(775,a,761,a)].
% 3.31/3.56 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(775,a,762,a)].
% 3.31/3.56 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),A) = A. [resolve(775,a,763,a)].
% 3.31/3.56 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(775,a,764,a)].
% 3.31/3.56 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(775,a,766,a)].
% 3.31/3.56 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(775,a,767,a)].
% 3.31/3.56 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(775,a,769,a)].
% 3.31/3.56 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(775,a,771,a)].
% 3.31/3.56 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(775,a,773,a)].
% 3.31/3.56 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(775,a,774,a)].
% 3.31/3.56 776 class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 3.31/3.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),A) = A. [resolve(776,a,733,a)].
% 3.31/3.56 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),A),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = A. [resolve(776,a,734,a)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(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(776,a,736,a)].
% 3.31/3.56 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),hAPP(c_Suc,B)). [resolve(776,a,738,a)].
% 3.31/3.56 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),hAPP(c_Suc,B)). [resolve(776,a,739,a)].
% 3.31/3.56 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(776,a,740,a)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(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(776,a,741,a)].
% 3.31/3.56 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(776,a,742,a)].
% 3.31/3.56 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(776,a,744,a)].
% 3.31/3.56 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(776,a,745,a)].
% 3.31/3.56 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(776,a,746,a)].
% 3.31/3.56 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(776,a,747,a)].
% 3.31/3.56 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(776,a,748,a)].
% 3.31/3.56 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(776,a,749,a)].
% 3.31/3.56 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(776,a,750,a)].
% 3.31/3.56 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(776,a,753,a)].
% 3.31/3.57 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(776,a,754,a)].
% 3.31/3.57 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(776,a,756,a)].
% 3.31/3.57 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(776,a,757,a)].
% 3.31/3.57 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(776,a,758,a)].
% 3.31/3.57 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(776,a,761,a)].
% 3.31/3.57 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(776,a,762,a)].
% 3.31/3.57 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),A) = A. [resolve(776,a,763,a)].
% 3.31/3.57 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = A. [resolve(776,a,764,a)].
% 3.31/3.57 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(776,a,766,a)].
% 3.31/3.57 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(776,a,767,a)].
% 3.31/3.57 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(776,a,769,a)].
% 3.31/3.57 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(776,a,771,a)].
% 3.31/3.57 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(776,a,773,a)].
% 3.31/3.57 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(776,a,774,a)].
% 3.40/3.66 777 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B. [resolve(18,b,28,b)].
% 3.40/3.66 778 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B. [resolve(18,b,29,b)].
% 3.40/3.66 779 -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). [resolve(18,b,32,b)].
% 3.40/3.66 780 -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). [resolve(18,b,33,b)].
% 3.40/3.66 781 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 3.40/3.66 782 -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].
% 3.40/3.66 783 -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].
% 3.40/3.66 784 -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].
% 3.40/3.66 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(781,a,782,a)].
% 3.40/3.66 785 class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 3.40/3.66 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(785,a,782,a)].
% 3.40/3.66 786 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 3.40/3.66 787 -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].
% 3.40/3.66 788 -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].
% 3.40/3.66 789 class_OrderedGroup_Omonoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 3.40/3.66 790 class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 3.40/3.66 791 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 3.40/3.66 792 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(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].
% 3.40/3.66 793 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(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].
% 3.40/3.66 794 -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].
% 3.40/3.66 795 -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].
% 3.40/3.66 796 -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].
% 3.40/3.66 797 -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].
% 3.40/3.66 798 -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].
% 3.40/3.66 799 -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].
% 3.40/3.66 800 -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].
% 3.40/3.66 801 -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].
% 3.40/3.66 802 -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].
% 3.40/3.66 803 -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].
% 3.40/3.66 804 -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].
% 3.40/3.66 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(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(791,a,792,a)].
% 3.40/3.66 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(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(791,a,793,a)].
% 3.40/3.66 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(791,a,794,a)].
% 3.40/3.66 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(791,a,795,a)].
% 3.40/3.66 Derived: -class_Int_Onumber(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),c_Int_Onumber__class_Onumber__of(A,tc_nat)),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),c_Int_Onumber__class_Onumber__of(A,tc_nat)),c_Int_Onumber__class_Onumber__of(A,tc_nat)). [resolve(791,a,796,a)].
% 3.40/3.66 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(791,a,799,a)].
% 3.40/3.66 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(791,a,800,a)].
% 3.40/3.66 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(791,a,803,a)].
% 3.40/3.66 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(791,a,804,a)].
% 3.40/3.66 805 class_OrderedGroup_Omonoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 3.40/3.66 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(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(805,a,792,a)].
% 3.40/3.66 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(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(805,a,793,a)].
% 3.40/3.66 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(805,a,794,a)].
% 3.40/3.66 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(805,a,795,a)].
% 3.40/3.66 Derived: -class_Int_Onumber(tc_Int_Oint) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)),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),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)). [resolve(805,a,796,a)].
% 3.40/3.66 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(805,a,799,a)].
% 3.40/3.66 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(805,a,800,a)].
% 3.40/3.66 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(805,a,803,a)].
% 3.44/3.69 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(805,a,804,a)].
% 3.44/3.69 806 class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 3.44/3.69 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(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(806,a,792,a)].
% 3.44/3.69 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),hAPP(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(806,a,793,a)].
% 3.44/3.69 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(806,a,794,a)].
% 3.44/3.69 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(806,a,795,a)].
% 3.44/3.69 Derived: -class_Int_Onumber(tc_Complex_Ocomplex) | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)),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),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex)). [resolve(806,a,796,a)].
% 3.44/3.69 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(806,a,799,a)].
% 3.44/3.69 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(806,a,800,a)].
% 3.44/3.69 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(806,a,803,a)].
% 3.44/3.69 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(806,a,804,a)].
% 3.44/3.69 807 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].
% 3.44/3.69 808 -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].
% 3.44/3.69 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(807,a,808,a)].
% 3.44/3.69 809 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].
% 3.54/3.78 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(809,a,808,a)].
% 3.54/3.78 810 class_RealVector_Oreal__field(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__RealVector_Oreal__field) # label(axiom). [assumption].
% 3.54/3.78 811 -class_RealVector_Oreal__field(A) | hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))),F) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),C),E)),F))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D)),F)),E)) # label(cls_DERIV__mult__lemma_0) # label(axiom). [assumption].
% 3.54/3.78 Derived: hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(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))),E) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),A),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),B),D)),E))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oinverse__class_Odivide(tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Complex_Ocomplex),A),C)),E)),D)). [resolve(810,a,811,a)].
% 3.54/3.78 812 class_Ring__and__Field_Oring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 3.54/3.78 813 -class_Ring__and__Field_Oring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(c_HOL_Ouminus__class_Ouminus(A),c_HOL_Oone__class_Oone(A))),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_power__minus_0) # label(axiom). [assumption].
% 3.54/3.78 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),A)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)). [resolve(812,a,813,a)].
% 3.54/3.78 814 class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) # label(axiom). [assumption].
% 3.54/3.78 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),A)),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),A),B)). [resolve(814,a,813,a)].
% 3.54/3.78 815 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 3.54/3.78 816 -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].
% 3.54/3.78 817 -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].
% 3.54/3.78 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(815,a,816,a)].
% 3.63/3.87 818 class_Ring__and__Field_Osemiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 3.63/3.87 819 class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 3.63/3.87 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(819,a,816,a)].
% 3.63/3.87 820 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.63/3.87 821 -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].
% 3.63/3.87 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(820,a,821,a)].
% 3.63/3.87 822 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.63/3.87 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(822,a,821,a)].
% 3.63/3.87 823 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.63/3.87 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(823,a,821,a)].
% 3.63/3.87 824 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 3.63/3.88 825 -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].
% 3.63/3.88 826 -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].
% 3.63/3.88 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(824,a,826,a)].
% 3.63/3.88 827 class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 3.63/3.88 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(827,a,826,a)].
% 3.63/3.88 828 class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 3.63/3.88 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(828,a,826,a)].
% 3.63/3.88 829 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 3.63/3.88 830 -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].
% 3.63/3.88 831 -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].
% 3.71/3.96 832 -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].
% 3.71/3.96 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(829,a,832,a)].
% 3.71/3.96 833 class_Ring__and__Field_Osemiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 3.71/3.96 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(833,a,832,a)].
% 3.71/3.96 834 class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 3.71/3.96 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(834,a,832,a)].
% 3.71/3.96 835 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 3.71/3.96 836 -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].
% 3.71/3.96 837 class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 3.71/3.96 838 class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 3.71/3.96 839 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 3.71/3.96 840 -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].
% 3.71/3.96 841 class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 3.71/3.96 842 class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 3.71/3.96 843 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 3.71/3.96 844 -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].
% 4.31/4.55 845 -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].
% 4.31/4.55 846 class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 4.31/4.55 847 class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 4.31/4.55 848 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 4.31/4.55 849 -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].
% 4.31/4.55 850 class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 4.31/4.55 851 class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 4.31/4.55 852 class_Int_Oring__char__0(tc_Int_Oint) # label(clsarity_Int__Oint__Int_Oring__char__0) # label(axiom). [assumption].
% 4.31/4.55 853 -class_Int_Oring__char__0(A) | -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_Int_Onumber__class_Onumber__of(C,A) | B = C # label(cls_eq__number__of_0) # label(axiom). [assumption].
% 4.31/4.55 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(852,a,853,a)].
% 4.31/4.55 854 class_Int_Oring__char__0(tc_Complex_Ocomplex) # label(clsarity_Complex__Ocomplex__Int_Oring__char__0) # label(axiom). [assumption].
% 4.31/4.55 Derived: -class_Int_Onumber__ring(tc_Complex_Ocomplex) | c_Int_Onumber__class_Onumber__of(A,tc_Complex_Ocomplex) != c_Int_Onumber__class_Onumber__of(B,tc_Complex_Ocomplex) | A = B. [resolve(854,a,853,a)].
% 4.31/4.55 855 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 4.31/4.55 856 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 4.31/4.55 Derived: A = A. [resolve(855,b,856,a)].
% 4.31/4.55
% 4.31/4.55 ============================== end predicate elimination =============
% 4.31/4.55
% 4.31/4.55 Auto_denials: (non-Horn, no changes).
% 4.31/4.55
% 4.31/4.55 Term ordering decisions:
% 4.31/4.55 Function symbol KB weights: tc_Int_Oint=1. tc_nat=1. tc_Complex_Ocomplex=1. c_Int_OPls=1. c_Suc=1. c_Int_OMin=1. c_Complex_Oii=1. v_a=1. v_i=1. v_m=1. hAPP=1. c_Int_Onumber__class_Onumber__of=1. tc_fun=1. c_Fact_Ofact__class_Ofact=1. c_HOL_Ozero__class_Ozero=1. c_HOL_Otimes__class_Otimes=1. c_HOL_Oplus__class_Oplus=1. c_Power_Opower__class_Opower=1. c_HOL_Ouminus__class_Ouminus=1. c_Int_OBit1=1. c_HOL_Oone__class_Oone=1. c_Int_OBit0=1. c_HOL_Ominus__class_Ominus=1. c_HOL_Oabs__class_Oabs=1. c_HOL_Oinverse__class_Odivide=1. c_FFT__Mirabelle_Oroot=1. c_Divides_Odiv__class_Odiv=1. c_SetInterval_Oord__class_OatLeastLessThan=1. c_FFT__Mirabelle_ODFT=1. c_FFT__Mirabelle_OIDFT=1. c_Finite__Set_Osetsum=1. c_COMBB=1. c_COMBC=1.
% 4.31/4.55
% 4.31/4.55 ============================== end of process initial clauses ========
% 4.31/4.55
% 4.31/4.55 ============================== CLAUSES FOR SEARCH ====================
% 4.31/4.55
% 4.31/4.55 ============================== end of clauses for search =============
% 4.31/4.55
% 4.31/4.55 ============================== SEARCH ================================
% 4.31/4.55
% 4.31/4.55 % Starting search at 2.70 seconds.
% 4.31/4.55
% 4.31/4.55 Low Water (keep): wt=123.000, iters=3725
% 4.31/4.55
% 4.31/4.55 Low Water (keep): wt=95.000, iters=3706
% 4.31/4.55
% 4.31/4.55 Low Water (keep): wt=84.000, iters=3679
% 4.31/4.55
% 4.31/4.55 Low Water (keep): wt=55.000, iters=3398
% 4.31/4.55
% 4.31/4.55 Low Water (keep): wt=51.000, iters=3371
% 4.31/4.55
% 4.31/4.55 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 55 (0.00 of 3.04 sec).
% 4.31/4.55
% 4.31/4.55 LowCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------