TSTP Solution File: SWV584-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV584-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 21:13:58 EDT 2022
% Result : Unsatisfiable 21.75s 22.00s
% Output : Refutation 21.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV584-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 14 20:03:50 EDT 2022
% 0.19/0.34 % CPUTime :
% 1.58/1.89 ============================== Prover9 ===============================
% 1.58/1.89 Prover9 (32) version 2009-11A, November 2009.
% 1.58/1.89 Process 7592 was started by sandbox on n023.cluster.edu,
% 1.58/1.89 Tue Jun 14 20:03:52 2022
% 1.58/1.89 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_7439_n023.cluster.edu".
% 1.58/1.89 ============================== end of head ===========================
% 1.58/1.89
% 1.58/1.89 ============================== INPUT =================================
% 1.58/1.89
% 1.58/1.89 % Reading from file /tmp/Prover9_7439_n023.cluster.edu
% 1.58/1.89
% 1.58/1.89 set(prolog_style_variables).
% 1.58/1.89 set(auto2).
% 1.58/1.89 % set(auto2) -> set(auto).
% 1.58/1.89 % set(auto) -> set(auto_inference).
% 1.58/1.89 % set(auto) -> set(auto_setup).
% 1.58/1.89 % set(auto_setup) -> set(predicate_elim).
% 1.58/1.89 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.58/1.89 % set(auto) -> set(auto_limits).
% 1.58/1.89 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.58/1.89 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.58/1.89 % set(auto) -> set(auto_denials).
% 1.58/1.89 % set(auto) -> set(auto_process).
% 1.58/1.89 % set(auto2) -> assign(new_constants, 1).
% 1.58/1.89 % set(auto2) -> assign(fold_denial_max, 3).
% 1.58/1.89 % set(auto2) -> assign(max_weight, "200.000").
% 1.58/1.89 % set(auto2) -> assign(max_hours, 1).
% 1.58/1.89 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.58/1.89 % set(auto2) -> assign(max_seconds, 0).
% 1.58/1.89 % set(auto2) -> assign(max_minutes, 5).
% 1.58/1.89 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.58/1.89 % set(auto2) -> set(sort_initial_sos).
% 1.58/1.89 % set(auto2) -> assign(sos_limit, -1).
% 1.58/1.89 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.58/1.89 % set(auto2) -> assign(max_megs, 400).
% 1.58/1.89 % set(auto2) -> assign(stats, some).
% 1.58/1.89 % set(auto2) -> clear(echo_input).
% 1.58/1.89 % set(auto2) -> set(quiet).
% 1.58/1.89 % set(auto2) -> clear(print_initial_clauses).
% 1.58/1.89 % set(auto2) -> clear(print_given).
% 1.58/1.89 assign(lrs_ticks,-1).
% 1.58/1.89 assign(sos_limit,10000).
% 1.58/1.89 assign(order,kbo).
% 1.58/1.89 set(lex_order_vars).
% 1.58/1.89 clear(print_given).
% 1.58/1.89
% 1.58/1.89 % formulas(sos). % not echoed (1685 formulas)
% 1.58/1.89
% 1.58/1.89 ============================== end of input ==========================
% 1.58/1.89
% 1.58/1.89 % From the command line: assign(max_seconds, 300).
% 1.58/1.89
% 1.58/1.89 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.58/1.89
% 1.58/1.89 % Formulas that are not ordinary clauses:
% 1.58/1.89
% 1.58/1.89 ============================== end of process non-clausal formulas ===
% 1.58/1.89
% 1.58/1.89 ============================== PROCESS INITIAL CLAUSES ===============
% 1.58/1.89
% 1.58/1.89 ============================== PREDICATE ELIMINATION =================
% 1.58/1.89 1 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.58/1.89 2 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),hAPP(c_Suc,D))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),D))),hAPP(B,D)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),D),C)) # label(cls_setsum__op__ivl__Suc_1) # label(axiom). [assumption].
% 1.58/1.89 3 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),D))),hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(D,tc_nat),E))) = hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),E)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),E)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) # label(cls_setsum__add__nat__ivl_0) # label(axiom). [assumption].
% 1.58/1.89 4 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,C)),hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,C),tc_nat),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),D)) # label(cls_setsum__head__upt__Suc_0) # label(axiom). [assumption].
% 1.58/1.89 5 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),C)),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),C)) # label(cls_comm__monoid__add_Opower__commutes_0) # label(axiom). [assumption].
% 1.58/1.89 6 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,C,A),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool))) = c_HOL_Ozero__class_Ozero(A) # label(cls_setsum__empty_0) # label(axiom). [assumption].
% 1.58/1.89 7 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,C,A),D) = c_HOL_Ozero__class_Ozero(A) | c_Finite__Set_Ofinite(D,C) # label(cls_setsum__def_1) # label(axiom). [assumption].
% 1.58/1.89 8 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,C,A),D) = c_HOL_Ozero__class_Ozero(A) | c_Finite__Set_Ofinite(D,C) # label(cls_setsum__infinite_0) # label(axiom). [assumption].
% 1.58/1.89 9 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),C)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),D)) # label(cls_comm__monoid__add_Opower__add_0) # label(axiom). [assumption].
% 1.58/1.89 10 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),D)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),C),D)) # label(cls_comm__monoid__add_Opower__mult__distrib_0) # label(axiom). [assumption].
% 1.58/1.89 11 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) # label(cls_add__increasing2_0) # label(axiom). [assumption].
% 1.58/1.89 12 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_add__increasing_0) # label(axiom). [assumption].
% 1.58/1.89 13 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),c_HOL_Oone__class_Oone(tc_nat)) = B # label(cls_comm__monoid__add_Opower__one__right_0) # label(axiom). [assumption].
% 1.58/1.89 14 -class_OrderedGroup_Ocomm__monoid__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_comm__monoid__add_Omult__left__commute_0) # label(axiom). [assumption].
% 1.58/1.89 15 -class_OrderedGroup_Ocomm__monoid__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_comm__monoid__add_Omult__assoc_0) # label(axiom). [assumption].
% 1.58/1.89 16 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) # label(cls_add__strict__increasing_0) # label(axiom). [assumption].
% 1.58/1.89 17 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_Finite__Set_Osetsum(B,C,A),c_Lattices_Oupper__semilattice__class_Osup(D,E,tc_fun(C,tc_bool)))),hAPP(c_Finite__Set_Osetsum(B,C,A),c_Lattices_Olower__semilattice__class_Oinf(D,E,tc_fun(C,tc_bool)))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_Finite__Set_Osetsum(B,C,A),D)),hAPP(c_Finite__Set_Osetsum(B,C,A),E)) | -c_Finite__Set_Ofinite(E,C) | -c_Finite__Set_Ofinite(D,C) # label(cls_setsum__Un__Int_0) # label(axiom). [assumption].
% 1.58/1.89 18 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_comm__monoid__add_Omult__commute_0) # label(axiom). [assumption].
% 1.58/1.89 19 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(D,tc_bool)) | -c_Finite__Set_Ofinite(C,D) | -c_Finite__Set_Ofinite(B,D) | hAPP(c_Finite__Set_Osetsum(E,D,A),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,tc_bool))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_Finite__Set_Osetsum(E,D,A),B)),hAPP(c_Finite__Set_Osetsum(E,D,A),C)) # label(cls_setsum__Un__disjoint_0) # label(axiom). [assumption].
% 1.58/1.89 20 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_comm__monoid__add_Opower__one_0) # label(axiom). [assumption].
% 1.58/1.89 21 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,C,A),c_Set_Oinsert(D,E,C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,D)),hAPP(c_Finite__Set_Osetsum(B,C,A),E)) | hBOOL(hAPP(hAPP(c_in(C),D),E)) | -c_Finite__Set_Ofinite(E,C) # label(cls_setsum__insert_0) # label(axiom). [assumption].
% 1.58/1.89 22 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_add__strict__increasing2_0) # label(axiom). [assumption].
% 1.58/1.89 23 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,C,A),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,E)),hAPP(c_Finite__Set_Osetsum(B,C,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(C,tc_bool)),D),c_Set_Oinsert(E,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C)))) | -hBOOL(hAPP(hAPP(c_in(C),E),D)) | -c_Finite__Set_Ofinite(D,C) # label(cls_setsum__diff1_H_0) # label(axiom). [assumption].
% 1.58/1.89 24 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_comm__monoid__add_Omult__1__right_0) # label(axiom). [assumption].
% 1.58/1.89 25 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_comm__monoid__add_Omult__1_0) # label(axiom). [assumption].
% 1.58/1.89 26 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),hAPP(c_Suc,D))) = c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),D),C)) # label(cls_setsum__op__ivl__Suc_0) # label(axiom). [assumption].
% 1.58/1.89 27 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(A) # label(cls_comm__monoid__add_Opower__0_0) # label(axiom). [assumption].
% 1.58/1.89 28 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),hAPP(c_Suc,C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),C)) # label(cls_comm__monoid__add_Opower__Suc_0) # label(axiom). [assumption].
% 1.58/1.89 29 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),hAPP(c_Suc,C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),C)),B) # label(cls_comm__monoid__add_Opower__Suc2_0) # label(axiom). [assumption].
% 1.58/1.89 30 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Oplus__class_Oplus(A)),C),B,A,A),D),B,A),E) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_Finite__Set_Osetsum(C,B,A),E)),hAPP(c_Finite__Set_Osetsum(D,B,A),E)) # label(cls_setsum__addf_0) # label(axiom). [assumption].
% 1.58/1.89 31 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),C)),D) # label(cls_comm__monoid__add_Opower__mult_0) # label(axiom). [assumption].
% 1.58/1.89 32 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B)),B) # label(cls_comm__monoid__add_Opower3__eq__cube_0) # label(axiom). [assumption].
% 1.58/1.89 33 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(B,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))),hAPP(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat))) # label(cls_Sum4_0) # label(axiom). [assumption].
% 1.58/1.89 34 -class_Power_Opower(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),hAPP(c_Power_Opower__class_Opower(A),B)),tc_nat,A,A),hAPP(hAPP(c_COMBB(tc_nat,A,tc_nat),hAPP(c_Power_Opower__class_Opower(A),C)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D))),tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,D))) = hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),hAPP(hAPP(c_COMBB(tc_nat,A,tc_nat),hAPP(c_Power_Opower__class_Opower(A),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D))),tc_nat,A,A),hAPP(c_Power_Opower__class_Opower(A),C)),tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,D))) # label(cls_lemma__realpow__rev__sumr_0) # label(axiom). [assumption].
% 1.58/1.89 35 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B) # label(cls_comm__monoid__add_Opower2__eq__square_0) # label(axiom). [assumption].
% 1.58/1.89 36 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),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_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),C)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) # label(cls_comm__monoid__add_Opower__even__eq_0) # label(axiom). [assumption].
% 1.58/1.89 37 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,C),tc_nat),hAPP(c_Suc,D))) = hAPP(c_Finite__Set_Osetsum(hAPP(hAPP(c_COMBB(tc_nat,A,tc_nat),B),c_Suc),tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),D)) # label(cls_setsum__shift__bounds__Suc__ivl_0) # label(axiom). [assumption].
% 1.58/1.89 38 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,C,A),D) = hAPP(c_Finite__Set_Osetsum(hAPP(hAPP(c_COMBB(tc_fun(C,tc_bool),A,E),c_Finite__Set_Osetsum(B,C,A)),hAPP(hAPP(c_COMBB(tc_fun(C,tc_bool),tc_fun(C,tc_bool),E),c_Collect(C)),hAPP(hAPP(c_COMBB(tc_fun(C,tc_bool),tc_fun(C,tc_bool),E),c_COMBS(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),C),c_and),hAPP(c_COMBC(c_in(C),C,tc_fun(C,tc_bool),tc_bool),D)),C,tc_bool,tc_bool)),c_COMBC(hAPP(hAPP(c_COMBB(E,tc_fun(E,tc_bool),C),c_fequal(E)),F),C,E,tc_bool)))),E,A),c_Set_Oimage(F,D,C,E)) | -c_Finite__Set_Ofinite(D,C) # label(cls_setsum__image__gen_0) # label(axiom). [assumption].
% 1.58/1.89 39 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),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_Oplus__class_Oplus(A),B),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),A),B),C)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) # label(cls_comm__monoid__add_Opower__odd__eq_0) # label(axiom). [assumption].
% 1.58/1.89 40 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(A) | hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),C)) = hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) # label(cls_setsum__shift__lb__Suc0__0__upt_0) # label(axiom). [assumption].
% 1.58/1.89 Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),hAPP(c_Suc,C))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C))),hAPP(A,C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),B)). [resolve(1,a,2,a)].
% 1.58/1.89 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C))),hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),D))) = hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(1,a,3,a)].
% 1.58/1.89 Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,B)),hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),tc_nat),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)). [resolve(1,a,4,a)].
% 1.58/1.89 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),B)),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),B)). [resolve(1,a,5,a)].
% 1.58/1.89 Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_nat),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,6,a)].
% 1.58/1.89 Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_nat),C) = c_HOL_Ozero__class_Ozero(tc_nat) | c_Finite__Set_Ofinite(C,B). [resolve(1,a,7,a)].
% 1.58/1.89 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),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_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),B)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),C)). [resolve(1,a,9,a)].
% 1.58/1.89 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),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_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),C)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),B),C)). [resolve(1,a,10,a)].
% 1.58/1.89 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(c_lessequals(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)). [resolve(1,a,11,b)].
% 1.58/1.89 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(c_lessequals(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(1,a,12,b)].
% 1.58/1.89 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(1,a,13,a)].
% 1.58/1.89 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(1,a,14,a)].
% 1.58/1.89 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(1,a,15,a)].
% 1.58/1.89 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)). [resolve(1,a,16,b)].
% 1.58/1.89 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Finite__Set_Osetsum(A,B,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(B,tc_bool)))),hAPP(c_Finite__Set_Osetsum(A,B,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,tc_bool)))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Finite__Set_Osetsum(A,B,tc_nat),C)),hAPP(c_Finite__Set_Osetsum(A,B,tc_nat),D)) | -c_Finite__Set_Ofinite(D,B) | -c_Finite__Set_Ofinite(C,B). [resolve(1,a,17,a)].
% 1.58/1.89 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(1,a,18,a)].
% 1.58/1.89 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)) | -c_Finite__Set_Ofinite(B,C) | -c_Finite__Set_Ofinite(A,C) | hAPP(c_Finite__Set_Osetsum(D,C,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_fun(C,tc_bool))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Finite__Set_Osetsum(D,C,tc_nat),A)),hAPP(c_Finite__Set_Osetsum(D,C,tc_nat),B)). [resolve(1,a,19,a)].
% 1.58/1.89 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,20,a)].
% 1.58/1.89 Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_nat),c_Set_Oinsert(C,D,B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,C)),hAPP(c_Finite__Set_Osetsum(A,B,tc_nat),D)) | hBOOL(hAPP(hAPP(c_in(B),C),D)) | -c_Finite__Set_Ofinite(D,B). [resolve(1,a,21,a)].
% 1.58/1.89 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(1,a,22,b)].
% 1.58/1.89 Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_nat),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,D)),hAPP(c_Finite__Set_Osetsum(A,B,tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(B,tc_bool)),C),c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B)))) | -hBOOL(hAPP(hAPP(c_in(B),D),C)) | -c_Finite__Set_Ofinite(C,B). [resolve(1,a,23,a)].
% 1.58/1.89 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(1,a,24,a)].
% 1.58/1.89 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(1,a,25,a)].
% 1.58/1.89 Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),hAPP(c_Suc,C))) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),B)). [resolve(1,a,26,a)].
% 1.58/1.89 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,27,a)].
% 1.58/1.89 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),hAPP(c_Suc,B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),B)). [resolve(1,a,28,a)].
% 1.58/1.89 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),hAPP(c_Suc,B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),B)),A). [resolve(1,a,29,a)].
% 1.58/1.89 Derived: hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),A),c_HOL_Oplus__class_Oplus(tc_nat)),B),A,tc_nat,tc_nat),C),A,tc_nat),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Finite__Set_Osetsum(B,A,tc_nat),D)),hAPP(c_Finite__Set_Osetsum(C,A,tc_nat),D)). [resolve(1,a,30,a)].
% 1.58/1.89 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),B)),C). [resolve(1,a,31,a)].
% 1.58/1.89 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),A)),A). [resolve(1,a,32,a)].
% 1.58/1.89 Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(A,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))),hAPP(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat))). [resolve(1,a,33,a)].
% 1.58/1.89 Derived: -class_Power_Opower(tc_nat) | hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(tc_nat)),hAPP(c_Power_Opower__class_Opower(tc_nat),A)),tc_nat,tc_nat,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_nat,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C))),tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,C))) = hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(tc_nat)),hAPP(hAPP(c_COMBB(tc_nat,tc_nat,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),A)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C))),tc_nat,tc_nat,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),B)),tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,C))). [resolve(1,a,34,b)].
% 1.58/1.90 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),A). [resolve(1,a,35,a)].
% 1.58/1.90 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),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_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(1,a,36,a)].
% 1.58/1.90 Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),tc_nat),hAPP(c_Suc,C))) = hAPP(c_Finite__Set_Osetsum(hAPP(hAPP(c_COMBB(tc_nat,tc_nat,tc_nat),A),c_Suc),tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C)). [resolve(1,a,37,a)].
% 1.58/1.90 Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_nat),C) = hAPP(c_Finite__Set_Osetsum(hAPP(hAPP(c_COMBB(tc_fun(B,tc_bool),tc_nat,D),c_Finite__Set_Osetsum(A,B,tc_nat)),hAPP(hAPP(c_COMBB(tc_fun(B,tc_bool),tc_fun(B,tc_bool),D),c_Collect(B)),hAPP(hAPP(c_COMBB(tc_fun(B,tc_bool),tc_fun(B,tc_bool),D),c_COMBS(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),B),c_and),hAPP(c_COMBC(c_in(B),B,tc_fun(B,tc_bool),tc_bool),C)),B,tc_bool,tc_bool)),c_COMBC(hAPP(hAPP(c_COMBB(D,tc_fun(D,tc_bool),B),c_fequal(D)),E),B,D,tc_bool)))),D,tc_nat),c_Set_Oimage(E,C,B,D)) | -c_Finite__Set_Ofinite(C,B). [resolve(1,a,38,a)].
% 1.58/1.90 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),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_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(tc_nat),tc_nat),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))). [resolve(1,a,39,a)].
% 1.58/1.90 Derived: hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),B)) = hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(1,a,40,a)].
% 1.58/1.90 41 class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.58/1.90 Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),hAPP(c_Suc,C))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C))),hAPP(A,C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),B)). [resolve(41,a,2,a)].
% 1.58/1.90 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C))),hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),D))) = hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(41,a,3,a)].
% 1.58/1.90 Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(A,B)),hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),tc_nat),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)). [resolve(41,a,4,a)].
% 1.58/1.90 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),B)),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),B)). [resolve(41,a,5,a)].
% 1.58/1.90 Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(41,a,6,a)].
% 1.58/1.90 Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),C) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_Finite__Set_Ofinite(C,B). [resolve(41,a,7,a)].
% 1.58/1.90 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),B)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),C)). [resolve(41,a,9,a)].
% 1.58/1.90 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),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_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),C)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),B),C)). [resolve(41,a,10,a)].
% 1.58/1.90 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)). [resolve(41,a,11,b)].
% 1.58/1.90 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(41,a,12,b)].
% 1.58/1.90 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(41,a,13,a)].
% 1.58/1.90 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(41,a,14,a)].
% 1.58/1.90 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(41,a,15,a)].
% 1.58/1.90 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),B)). [resolve(41,a,16,b)].
% 1.58/1.90 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(B,tc_bool)))),hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,tc_bool)))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),C)),hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),D)) | -c_Finite__Set_Ofinite(D,B) | -c_Finite__Set_Ofinite(C,B). [resolve(41,a,17,a)].
% 1.58/1.90 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(41,a,18,a)].
% 1.58/1.90 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)) | -c_Finite__Set_Ofinite(B,C) | -c_Finite__Set_Ofinite(A,C) | hAPP(c_Finite__Set_Osetsum(D,C,tc_Int_Oint),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_fun(C,tc_bool))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Finite__Set_Osetsum(D,C,tc_Int_Oint),A)),hAPP(c_Finite__Set_Osetsum(D,C,tc_Int_Oint),B)). [resolve(41,a,19,a)].
% 1.58/1.90 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(41,a,20,a)].
% 1.58/1.90 Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),c_Set_Oinsert(C,D,B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(A,C)),hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),D)) | hBOOL(hAPP(hAPP(c_in(B),C),D)) | -c_Finite__Set_Ofinite(D,B). [resolve(41,a,21,a)].
% 1.58/1.90 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(41,a,22,b)].
% 1.58/1.90 Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(A,D)),hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(B,tc_bool)),C),c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B)))) | -hBOOL(hAPP(hAPP(c_in(B),D),C)) | -c_Finite__Set_Ofinite(C,B). [resolve(41,a,23,a)].
% 1.58/1.90 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(41,a,24,a)].
% 1.58/1.90 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A) = A. [resolve(41,a,25,a)].
% 1.58/1.90 Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),hAPP(c_Suc,C))) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),B)). [resolve(41,a,26,a)].
% 1.58/1.90 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(41,a,27,a)].
% 1.58/1.90 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),hAPP(c_Suc,B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),B)). [resolve(41,a,28,a)].
% 1.58/1.90 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),hAPP(c_Suc,B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),B)),A). [resolve(41,a,29,a)].
% 1.58/1.90 Derived: hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),A),c_HOL_Oplus__class_Oplus(tc_Int_Oint)),B),A,tc_Int_Oint,tc_Int_Oint),C),A,tc_Int_Oint),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Finite__Set_Osetsum(B,A,tc_Int_Oint),D)),hAPP(c_Finite__Set_Osetsum(C,A,tc_Int_Oint),D)). [resolve(41,a,30,a)].
% 1.58/1.90 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),B)),C). [resolve(41,a,31,a)].
% 1.58/1.90 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),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_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A)),A). [resolve(41,a,32,a)].
% 1.58/1.90 Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(A,c_HOL_Oone__class_Oone(tc_nat)))),hAPP(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))),hAPP(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat))). [resolve(41,a,33,a)].
% 1.58/1.90 Derived: -class_Power_Opower(tc_Int_Oint) | hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),c_HOL_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A)),tc_nat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_nat,tc_Int_Oint,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C))),tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,C))) = hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),c_HOL_Otimes__class_Otimes(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_nat,tc_Int_Oint,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C))),tc_nat,tc_Int_Oint,tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B)),tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,C))). [resolve(41,a,34,b)].
% 1.58/1.90 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),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_Oplus__class_Oplus(tc_Int_Oint),A),A). [resolve(41,a,35,a)].
% 1.58/1.90 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),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_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)). [resolve(41,a,36,a)].
% 1.58/1.90 Derived: hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),tc_nat),hAPP(c_Suc,C))) = hAPP(c_Finite__Set_Osetsum(hAPP(hAPP(c_COMBB(tc_nat,tc_Int_Oint,tc_nat),A),c_Suc),tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C)). [resolve(41,a,37,a)].
% 1.58/1.90 Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),C) = hAPP(c_Finite__Set_Osetsum(hAPP(hAPP(c_COMBB(tc_fun(B,tc_bool),tc_Int_Oint,D),c_Finite__Set_Osetsum(A,B,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_fun(B,tc_bool),tc_fun(B,tc_bool),D),c_Collect(B)),hAPP(hAPP(c_COMBB(tc_fun(B,tc_bool),tc_fun(B,tc_bool),D),c_COMBS(hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),B),c_and),hAPP(c_COMBC(c_in(B),B,tc_fun(B,tc_bool),tc_bool),C)),B,tc_bool,tc_bool)),c_COMBC(hAPP(hAPP(c_COMBB(D,tc_fun(D,tc_bool),B),c_fequal(D)),E),B,D,tc_bool)))),D,tc_Int_Oint),c_Set_Oimage(E,C,B,D)) | -c_Finite__Set_Ofinite(C,B). [resolve(41,a,38,a)].
% 1.74/1.99 Derived: hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),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_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oplus__class_Oplus(tc_Int_Oint),tc_Int_Oint),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))). [resolve(41,a,39,a)].
% 1.74/1.99 Derived: hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),B)) = hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(41,a,40,a)].
% 1.74/1.99 42 class_Int_Onumber__ring(tc_Int_Oint) # label(clsarity_Int__Oint__Int_Onumber__ring) # label(axiom). [assumption].
% 1.74/1.99 43 -class_Int_Onumber__ring(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) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) # label(cls_neg__one__even__power_0) # label(axiom). [assumption].
% 1.74/1.99 44 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Int_Onumber__class_Onumber__of(B,A)),c_Int_Onumber__class_Onumber__of(C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),B),C)) # label(cls_less__number__of_1) # label(axiom). [assumption].
% 1.74/1.99 45 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Int_Onumber__class_Onumber__of(B,A)),c_Int_Onumber__class_Onumber__of(C,A))) # label(cls_less__number__of_0) # label(axiom). [assumption].
% 1.74/1.99 46 -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].
% 1.74/1.99 47 -class_Int_Onumber__ring(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Int_Onumber__class_Onumber__of(c_Int_OMin,A)),B) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,A) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) # label(cls_neg__one__odd__power_0) # label(axiom). [assumption].
% 1.74/1.99 48 -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].
% 1.74/1.99 49 -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].
% 1.74/1.99 50 -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].
% 1.74/1.99 51 -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].
% 1.74/1.99 52 -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].
% 1.74/1.99 53 -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].
% 1.74/1.99 54 -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].
% 1.74/1.99 55 -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].
% 1.74/1.99 56 -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].
% 1.74/1.99 57 -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(c_Int_OBit1(B),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_Int_Onumber__class_Onumber__of(B,A))),c_Int_Onumber__class_Onumber__of(B,A)) # label(cls_number__of__Bit1_0) # label(axiom). [assumption].
% 1.74/1.99 58 -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OPls,A)) = B # label(cls_add__numeral__0__right_0) # label(axiom). [assumption].
% 1.74/1.99 59 -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Int_Onumber__class_Onumber__of(c_Int_OPls,A)),B) = B # label(cls_add__numeral__0_0) # label(axiom). [assumption].
% 1.74/1.99 60 -class_Int_Onumber__ring(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(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)))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),A)),B)),C)) # label(cls_power2__diff_0) # label(axiom). [assumption].
% 1.74/1.99 61 -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A)) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),A) # label(cls_one__add__one__is__two_0) # label(axiom). [assumption].
% 1.74/1.99 62 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Int_Onumber__class_Onumber__of(B,A)),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),B),c_Int_OBit1(c_Int_OPls))) # label(cls_less__special_I4_J_1) # label(axiom). [assumption].
% 1.74/1.99 63 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),B),c_Int_OBit1(c_Int_OPls))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Int_Onumber__class_Onumber__of(B,A)),c_HOL_Oone__class_Oone(A))) # label(cls_less__special_I4_J_0) # label(axiom). [assumption].
% 1.74/1.99 64 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),c_Int_Onumber__class_Onumber__of(B,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),B)) # label(cls_less__special_I2_J_1) # label(axiom). [assumption].
% 1.74/1.99 65 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),c_Int_Onumber__class_Onumber__of(B,A))) # label(cls_less__special_I2_J_0) # label(axiom). [assumption].
% 1.74/1.99 66 -class_Int_Onumber__ring(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Int_Onumber__class_Onumber__of(c_Int_OMin,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__m1__even_0) # label(axiom). [assumption].
% 1.74/1.99 67 -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(c_Int_OBit0(B),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(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_number__of__Bit0_0) # label(axiom). [assumption].
% 1.74/1.99 68 -class_Int_Onumber__ring(A) | c_HOL_Oone__class_Oone(A) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),A) # label(cls_comp__arith_I110_J_0) # label(axiom). [assumption].
% 1.74/1.99 69 -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),A) = c_HOL_Oone__class_Oone(A) # label(cls_numeral__1__eq__1_0) # label(axiom). [assumption].
% 1.74/1.99 70 -class_Int_Onumber__ring(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(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)))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),A)),B)),C)) # label(cls_power2__sum_0) # label(axiom). [assumption].
% 1.74/1.99 71 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Int_Onumber__class_Onumber__of(B,A)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),B),c_Int_OPls)) # label(cls_less__special_I3_J_1) # label(axiom). [assumption].
% 1.74/1.99 72 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),B),c_Int_OPls)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Int_Onumber__class_Onumber__of(B,A)),c_HOL_Ozero__class_Ozero(A))) # label(cls_less__special_I3_J_0) # label(axiom). [assumption].
% 1.74/1.99 73 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),B)) # label(cls_less__special_I1_J_1) # label(axiom). [assumption].
% 1.74/1.99 74 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,A))) # label(cls_less__special_I1_J_0) # label(axiom). [assumption].
% 1.74/1.99 75 -class_Int_Onumber__ring(A) | 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))),c_Int_Onumber__class_Onumber__of(B,A)) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(B),A) # label(cls_double__number__of__Bit0_0) # label(axiom). [assumption].
% 1.74/1.99 76 -class_Int_Onumber__ring(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Int_Onumber__class_Onumber__of(c_Int_OMin,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_Int_Onumber__class_Onumber__of(c_Int_OMin,A) # label(cls_power__m1__odd_0) # label(axiom). [assumption].
% 1.74/1.99 77 -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),A)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B) # label(cls_mult__2__right_0) # label(axiom). [assumption].
% 1.74/1.99 78 -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),A)),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B) # label(cls_mult__2_0) # label(axiom). [assumption].
% 1.74/1.99 79 -class_Int_Onumber__ring(A) | c_HOL_Ozero__class_Ozero(A) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,A) # label(cls_comp__arith_I112_J_0) # label(axiom). [assumption].
% 1.74/1.99 80 -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(c_Int_OPls,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_number__of__Pls_0) # label(axiom). [assumption].
% 1.74/1.99 81 -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),A)),B) = B # label(cls_mult__numeral__1_0) # label(axiom). [assumption].
% 1.74/1.99 82 -class_Int_Onumber__ring(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),A)) = B # label(cls_mult__numeral__1__right_0) # label(axiom). [assumption].
% 1.74/1.99 83 -class_Int_Oring__char__0(A) | -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_Int_Onumber__class_Onumber__of(C,A) | B = C # label(cls_eq__number__of_0) # label(axiom). [assumption].
% 1.74/1.99 Derived: 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) | -c_Parity_Oeven__odd__class_Oeven(A,tc_nat). [resolve(42,a,43,a)].
% 1.74/1.99 Derived: -class_Ring__and__Field_Oordered__idom(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),B)). [resolve(42,a,44,b)].
% 1.74/1.99 Derived: -class_Ring__and__Field_Oordered__idom(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint))). [resolve(42,a,45,b)].
% 1.74/1.99 Derived: -class_Ring__and__Field_Oidom(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(42,a,46,b)].
% 1.74/1.99 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint)),A) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint) | c_Parity_Oeven__odd__class_Oeven(A,tc_nat). [resolve(42,a,47,a)].
% 1.74/1.99 Derived: -class_Ring__and__Field_Oidom(tc_Int_Oint) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(42,a,48,b)].
% 1.74/1.99 Derived: -class_Ring__and__Field_Oidom(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(42,a,49,b)].
% 1.74/1.99 Derived: -class_Ring__and__Field_Oidom(tc_Int_Oint) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = B. [resolve(42,a,50,b)].
% 1.74/1.99 Derived: -class_Ring__and__Field_Oidom(tc_Int_Oint) | A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)). [resolve(42,a,51,b)].
% 1.74/1.99 Derived: -class_Ring__and__Field_Oidom(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(42,a,52,b)].
% 1.74/1.99 Derived: -class_Ring__and__Field_Oidom(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(42,a,53,b)].
% 1.74/1.99 Derived: c_Int_Onumber__class_Onumber__of(c_Int_OBit1(A),tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint))),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)). [resolve(42,a,57,a)].
% 1.74/1.99 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Int_Oint)) = A. [resolve(42,a,58,a)].
% 1.74/1.99 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Int_Oint)),A) = A. [resolve(42,a,59,a)].
% 1.74/1.99 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(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)))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_Int_Oint)),A)),B)). [resolve(42,a,60,a)].
% 1.74/1.99 Derived: 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)) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_Int_Oint). [resolve(42,a,61,a)].
% 1.74/1.99 Derived: -class_Ring__and__Field_Oordered__idom(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),c_Int_OBit1(c_Int_OPls))). [resolve(42,a,62,b)].
% 1.74/1.99 Derived: -class_Ring__and__Field_Oordered__idom(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),c_Int_OBit1(c_Int_OPls))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)),c_HOL_Oone__class_Oone(tc_Int_Oint))). [resolve(42,a,63,b)].
% 1.74/1.99 Derived: -class_Ring__and__Field_Oordered__idom(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),A)). [resolve(42,a,64,b)].
% 1.74/1.99 Derived: -class_Ring__and__Field_Oordered__idom(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint))). [resolve(42,a,65,b)].
% 1.74/1.99 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(c_Int_OMin,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(42,a,66,a)].
% 1.74/1.99 Derived: c_Int_Onumber__class_Onumber__of(c_Int_OBit0(A),tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint))),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)). [resolve(42,a,67,a)].
% 1.74/1.99 Derived: c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_Int_Oint). [resolve(42,a,68,a)].
% 1.74/1.99 Derived: c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_Int_Oint) = c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(42,a,69,a)].
% 1.74/2.07 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(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)))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_Int_Oint)),A)),B)). [resolve(42,a,70,a)].
% 1.74/2.07 Derived: -class_Ring__and__Field_Oordered__idom(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),c_Int_OPls)). [resolve(42,a,71,b)].
% 1.74/2.07 Derived: -class_Ring__and__Field_Oordered__idom(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),c_Int_OPls)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(42,a,72,b)].
% 1.74/2.07 Derived: -class_Ring__and__Field_Oordered__idom(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),A)). [resolve(42,a,73,b)].
% 1.74/2.07 Derived: -class_Ring__and__Field_Oordered__idom(tc_Int_Oint) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint))). [resolve(42,a,74,b)].
% 1.74/2.07 Derived: 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))),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint)) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(A),tc_Int_Oint). [resolve(42,a,75,a)].
% 1.74/2.07 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(c_Int_OMin,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))) = c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_Int_Oint). [resolve(42,a,76,a)].
% 1.74/2.07 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_Int_Oint)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A). [resolve(42,a,77,a)].
% 1.74/2.07 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_Int_Oint)),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A). [resolve(42,a,78,a)].
% 1.74/2.07 Derived: c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Int_Oint). [resolve(42,a,79,a)].
% 1.74/2.07 Derived: c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(42,a,80,a)].
% 1.74/2.07 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_Int_Oint)),A) = A. [resolve(42,a,81,a)].
% 1.74/2.07 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_Int_Oint)) = A. [resolve(42,a,82,a)].
% 1.74/2.07 Derived: -class_Int_Oring__char__0(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint) | A = B. [resolve(42,a,83,b)].
% 1.74/2.07 84 class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 1.74/2.07 85 -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) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),D),E)) # label(cls_less__eqI_1) # label(axiom). [assumption].
% 1.74/2.07 86 -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) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),D),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_less__eqI_0) # label(axiom). [assumption].
% 1.74/2.07 87 -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) | hBOOL(hAPP(c_lessequals(C,A),B)) | -hBOOL(hAPP(c_lessequals(E,A),D)) # label(cls_le__eqI_1) # label(axiom). [assumption].
% 1.74/2.07 88 -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) | hBOOL(hAPP(c_lessequals(E,A),D)) | -hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_le__eqI_0) # label(axiom). [assumption].
% 1.74/2.07 89 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_le__iff__diff__le__0_0) # label(axiom). [assumption].
% 1.74/2.07 90 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_le__iff__diff__le__0_1) # label(axiom). [assumption].
% 1.74/2.07 91 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_less__iff__diff__less__0_0) # label(axiom). [assumption].
% 1.74/2.07 92 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C)),c_HOL_Ozero__class_Ozero(A))) # label(cls_less__iff__diff__less__0_1) # label(axiom). [assumption].
% 1.74/2.07 93 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(E,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E))) # label(cls_le__add__right__mono_0) # label(axiom). [assumption].
% 1.74/2.07 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) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),C),D)). [resolve(84,a,85,a)].
% 1.74/2.07 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) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),C),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),B)). [resolve(84,a,86,a)].
% 1.74/2.07 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) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(D,tc_Int_Oint),C)). [resolve(84,a,87,a)].
% 1.74/2.07 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) | hBOOL(hAPP(c_lessequals(D,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(84,a,88,a)].
% 1.74/2.07 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(84,a,89,a)].
% 1.74/2.07 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(84,a,90,a)].
% 1.74/2.07 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),B)). [resolve(84,a,91,a)].
% 1.88/2.16 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(84,a,92,a)].
% 1.88/2.16 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))) | -hBOOL(hAPP(c_lessequals(D,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),D))). [resolve(84,a,93,a)].
% 1.88/2.16 94 class_Divides_Osemiring__div(tc_nat) # label(clsarity_nat__Divides_Osemiring__div) # label(axiom). [assumption].
% 1.88/2.16 95 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) # label(cls_zmod__simps_I2_J_0) # label(axiom). [assumption].
% 1.88/2.16 96 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,C,A)),D),C,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A) # label(cls_zmod__simps_I1_J_0) # label(axiom). [assumption].
% 1.88/2.16 97 -class_Divides_Osemiring__div(A) | B = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(B,C,A)),C)),c_Divides_Odiv__class_Omod(B,C,A)) # label(cls_mod__div__decomp_0) # label(axiom). [assumption].
% 1.88/2.16 98 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(B,C,A)),C)),c_Divides_Odiv__class_Omod(B,C,A)) = B # label(cls_mod__div__equality_0) # label(axiom). [assumption].
% 1.88/2.16 99 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Odiv(C,B,A))),c_Divides_Odiv__class_Omod(C,B,A)) = C # label(cls_mod__div__equality2_0) # label(axiom). [assumption].
% 1.88/2.16 100 -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].
% 1.88/2.16 101 -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].
% 1.88/2.16 102 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__add__self2_0) # label(axiom). [assumption].
% 1.88/2.16 103 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),B,A) = c_Divides_Odiv__class_Omod(C,B,A) # label(cls_mod__add__self1_0) # label(axiom). [assumption].
% 1.88/2.16 104 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,D,A)),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__add__eq_0) # label(axiom). [assumption].
% 1.88/2.16 105 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,A),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__mod__trivial_0) # label(axiom). [assumption].
% 1.88/2.16 106 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__self_0) # label(axiom). [assumption].
% 1.88/2.16 107 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(B,C,A)),C)),c_Divides_Odiv__class_Omod(B,C,A))),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) # label(cls_div__mod__equality_0) # label(axiom). [assumption].
% 1.88/2.16 108 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Odiv(C,B,A))),c_Divides_Odiv__class_Omod(C,B,A))),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D) # label(cls_div__mod__equality2_0) # label(axiom). [assumption].
% 1.88/2.16 109 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(B,C,A),C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__div__trivial_0) # label(axiom). [assumption].
% 1.88/2.16 110 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(E,C,A) != c_Divides_Odiv__class_Omod(F,C,A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),E),B),C,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),F),D),C,A) # label(cls_mod__add__cong_0) # label(axiom). [assumption].
% 1.88/2.16 111 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Oone__class_Oone(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__by__1_0) # label(axiom). [assumption].
% 1.88/2.16 112 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__add__right__eq_0) # label(axiom). [assumption].
% 1.88/2.16 113 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,D,A)),C),D,A) # label(cls_mod__add__left__eq_0) # label(axiom). [assumption].
% 1.88/2.16 114 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__mult__self2_0) # label(axiom). [assumption].
% 1.88/2.16 115 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),D,A) = c_Divides_Odiv__class_Omod(B,D,A) # label(cls_mod__mult__self1_0) # label(axiom). [assumption].
% 1.88/2.16 116 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Oone__class_Oone(A),A) = B # label(cls_div__by__1_0) # label(axiom). [assumption].
% 1.88/2.16 117 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__self_0) # label(axiom). [assumption].
% 1.88/2.16 118 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_mod__by__0_0) # label(axiom). [assumption].
% 1.88/2.16 119 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__by__0_0) # label(axiom). [assumption].
% 1.88/2.16 120 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__0_0) # label(axiom). [assumption].
% 1.88/2.16 121 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__0_0) # label(axiom). [assumption].
% 1.88/2.16 122 -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].
% 1.88/2.16 123 -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].
% 1.88/2.16 124 -class_Divides_Osemiring__div(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,C,A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(B,C,A)),C)) = B # label(cls_semiring__div__class_Omod__div__equality_H_0) # label(axiom). [assumption].
% 1.88/2.16 125 -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].
% 1.88/2.16 126 -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].
% 1.88/2.16 127 -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].
% 1.88/2.16 128 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(B,D,A)),C) # label(cls_mod__mult__mult2_0) # label(axiom). [assumption].
% 1.88/2.16 129 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Omod(C,D,A)) # label(cls_mod__mult__mult1_0) # label(axiom). [assumption].
% 1.88/2.16 130 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(E,C,A) != c_Divides_Odiv__class_Omod(F,C,A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),B),C,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),F),D),C,A) # label(cls_mod__mult__cong_0) # label(axiom). [assumption].
% 1.88/2.16 131 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(B,D,A)),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__mult__eq_0) # label(axiom). [assumption].
% 1.88/2.16 132 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(B,C,A)),D),C,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),C,A) # label(cls_zmod__simps_I4_J_0) # label(axiom). [assumption].
% 1.88/2.16 133 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__mult__right__eq_0) # label(axiom). [assumption].
% 1.88/2.16 134 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(B,D,A)),C),D,A) # label(cls_mod__mult__left__eq_0) # label(axiom). [assumption].
% 1.88/2.16 135 -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].
% 1.88/2.16 136 -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].
% 1.88/2.16 137 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__mult__self1__is__0_0) # label(axiom). [assumption].
% 1.88/2.16 138 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__mult__self2__is__0_0) # label(axiom). [assumption].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat). [resolve(94,a,95,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),C),B,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat). [resolve(94,a,96,a)].
% 1.88/2.16 Derived: A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),B)),c_Divides_Odiv__class_Omod(A,B,tc_nat)). [resolve(94,a,97,a)].
% 1.88/2.16 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),B)),c_Divides_Odiv__class_Omod(A,B,tc_nat)) = A. [resolve(94,a,98,a)].
% 1.88/2.16 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Divides_Odiv__class_Odiv(B,A,tc_nat))),c_Divides_Odiv__class_Omod(B,A,tc_nat)) = B. [resolve(94,a,99,a)].
% 1.88/2.16 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(94,a,100,a)].
% 1.88/2.16 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(94,a,101,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat). [resolve(94,a,102,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat) = c_Divides_Odiv__class_Omod(B,A,tc_nat). [resolve(94,a,103,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,C,tc_nat)),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat). [resolve(94,a,104,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat). [resolve(94,a,105,a)].
% 1.88/2.16 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(94,a,106,a)].
% 1.88/2.16 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),B)),c_Divides_Odiv__class_Omod(A,B,tc_nat))),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C). [resolve(94,a,107,a)].
% 1.88/2.16 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Divides_Odiv__class_Odiv(B,A,tc_nat))),c_Divides_Odiv__class_Omod(B,A,tc_nat))),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C). [resolve(94,a,108,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(A,B,tc_nat),B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(94,a,109,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(A,B,tc_nat) != c_Divides_Odiv__class_Omod(C,B,tc_nat) | c_Divides_Odiv__class_Omod(D,B,tc_nat) != c_Divides_Odiv__class_Omod(E,B,tc_nat) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),A),B,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),E),C),B,tc_nat). [resolve(94,a,110,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(94,a,111,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat). [resolve(94,a,112,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,C,tc_nat)),B),C,tc_nat). [resolve(94,a,113,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat). [resolve(94,a,114,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)),C,tc_nat) = c_Divides_Odiv__class_Omod(A,C,tc_nat). [resolve(94,a,115,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = A. [resolve(94,a,116,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(A,A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(94,a,117,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A. [resolve(94,a,118,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(94,a,119,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(94,a,120,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(94,a,121,a)].
% 1.88/2.16 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(94,a,122,a)].
% 1.88/2.16 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(94,a,123,a)].
% 1.88/2.16 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),B)) = A. [resolve(94,a,124,a)].
% 1.88/2.16 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(94,a,125,a)].
% 1.88/2.16 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(94,a,126,a)].
% 1.88/2.16 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(94,a,127,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Omod(A,C,tc_nat)),B). [resolve(94,a,128,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Divides_Odiv__class_Omod(B,C,tc_nat)). [resolve(94,a,129,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(A,B,tc_nat) != c_Divides_Odiv__class_Omod(C,B,tc_nat) | c_Divides_Odiv__class_Omod(D,B,tc_nat) != c_Divides_Odiv__class_Omod(E,B,tc_nat) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),D),A),B,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),E),C),B,tc_nat). [resolve(94,a,130,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Omod(A,C,tc_nat)),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat). [resolve(94,a,131,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),C),B,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),B,tc_nat). [resolve(94,a,132,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Divides_Odiv__class_Omod(B,C,tc_nat)),C,tc_nat). [resolve(94,a,133,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),C,tc_nat) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Divides_Odiv__class_Omod(A,C,tc_nat)),B),C,tc_nat). [resolve(94,a,134,a)].
% 1.88/2.16 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(94,a,135,a)].
% 1.88/2.16 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(94,a,136,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(94,a,137,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(94,a,138,a)].
% 1.88/2.16 139 class_Divides_Osemiring__div(tc_Int_Oint) # label(clsarity_Int__Oint__Divides_Osemiring__div) # label(axiom). [assumption].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),C,tc_Int_Oint). [resolve(139,a,95,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint)),C),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C),B,tc_Int_Oint). [resolve(139,a,96,a)].
% 1.88/2.16 Derived: A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint)),B)),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint)). [resolve(139,a,97,a)].
% 1.88/2.16 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint)),B)),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint)) = A. [resolve(139,a,98,a)].
% 1.88/2.16 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Odiv(B,A,tc_Int_Oint))),c_Divides_Odiv__class_Omod(B,A,tc_Int_Oint)) = B. [resolve(139,a,99,a)].
% 1.88/2.16 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(139,a,100,a)].
% 1.88/2.16 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(139,a,101,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint). [resolve(139,a,102,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),A,tc_Int_Oint) = c_Divides_Odiv__class_Omod(B,A,tc_Int_Oint). [resolve(139,a,103,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint)),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)),C,tc_Int_Oint). [resolve(139,a,104,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint). [resolve(139,a,105,a)].
% 1.88/2.16 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(139,a,106,a)].
% 1.88/2.16 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint)),B)),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint))),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C). [resolve(139,a,107,a)].
% 1.88/2.16 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Odiv(B,A,tc_Int_Oint))),c_Divides_Odiv__class_Omod(B,A,tc_Int_Oint))),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C). [resolve(139,a,108,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),B,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(139,a,109,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(C,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(D,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(E,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),D),A),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),E),C),B,tc_Int_Oint). [resolve(139,a,110,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(139,a,111,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)),C,tc_Int_Oint). [resolve(139,a,112,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint)),B),C,tc_Int_Oint). [resolve(139,a,113,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(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) = c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint). [resolve(139,a,114,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(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) = c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint). [resolve(139,a,115,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = A. [resolve(139,a,116,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(A,A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(139,a,117,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = A. [resolve(139,a,118,a)].
% 1.88/2.16 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(139,a,119,a)].
% 1.88/2.16 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(139,a,120,a)].
% 1.88/2.16 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(139,a,121,a)].
% 1.88/2.16 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(139,a,122,a)].
% 1.88/2.16 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(139,a,123,a)].
% 1.88/2.17 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Odiv(A,B,tc_Int_Oint)),B)) = A. [resolve(139,a,124,a)].
% 1.88/2.17 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(139,a,125,a)].
% 1.88/2.17 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(139,a,126,a)].
% 1.88/2.17 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(139,a,127,a)].
% 1.88/2.17 Derived: c_Divides_Odiv__class_Omod(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) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint)),B). [resolve(139,a,128,a)].
% 1.88/2.17 Derived: c_Divides_Odiv__class_Omod(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) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)). [resolve(139,a,129,a)].
% 1.88/2.17 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(C,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(D,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(E,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),A),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),E),C),B,tc_Int_Oint). [resolve(139,a,130,a)].
% 1.88/2.17 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint)),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)),C,tc_Int_Oint). [resolve(139,a,131,a)].
% 1.88/2.17 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint)),C),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),B,tc_Int_Oint). [resolve(139,a,132,a)].
% 1.88/2.17 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)),C,tc_Int_Oint). [resolve(139,a,133,a)].
% 1.88/2.17 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint)),B),C,tc_Int_Oint). [resolve(139,a,134,a)].
% 1.88/2.17 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(139,a,135,a)].
% 1.88/2.17 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(139,a,136,a)].
% 1.88/2.17 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(139,a,137,a)].
% 1.88/2.17 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),B,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(139,a,138,a)].
% 1.98/2.25 140 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.98/2.25 141 -class_Orderings_Olinorder(A) | B = C | -hBOOL(hAPP(c_lessequals(B,A),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 1.98/2.25 142 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 1.98/2.25 143 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 1.98/2.25 144 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 1.98/2.25 145 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | C = B | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 1.98/2.25 146 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 1.98/2.25 147 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.98/2.25 148 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_not__leE_0) # label(axiom). [assumption].
% 1.98/2.25 149 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_lessequals(B,A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 1.98/2.25 150 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) | hBOOL(hAPP(c_lessequals(B,A),B)) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 1.98/2.25 151 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 1.98/2.25 152 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 1.98/2.25 153 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 1.98/2.25 154 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 1.98/2.25 155 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Int_Onumber__class_Onumber__of(B,A)),c_Int_Onumber__class_Onumber__of(C,A))) | -hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(C,A),A),c_Int_Onumber__class_Onumber__of(B,A))) # label(cls_le__number__of__eq__not__less_0) # label(axiom). [assumption].
% 1.98/2.25 156 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),A),c_Int_Onumber__class_Onumber__of(C,A))) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Int_Onumber__class_Onumber__of(C,A)),c_Int_Onumber__class_Onumber__of(B,A))) # label(cls_le__number__of__eq__not__less_1) # label(axiom). [assumption].
% 1.98/2.25 157 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(A,tc_bool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,A),C)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,A),D)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(D,A),C) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_ivl__diff_0) # label(axiom). [assumption].
% 1.98/2.25 158 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 1.98/2.25 159 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 1.98/2.25 160 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,A),C),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,A),D),tc_fun(A,tc_bool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,A),D) | -hBOOL(hAPP(c_lessequals(C,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_ivl__disj__un_I17_J_0) # label(axiom). [assumption].
% 1.98/2.25 Derived: A = B | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)). [resolve(140,a,141,a)].
% 1.98/2.25 Derived: A = B | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),A)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)). [resolve(140,a,143,a)].
% 1.98/2.25 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),A)). [resolve(140,a,147,a)].
% 1.98/2.25 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(140,a,148,a)].
% 1.98/2.25 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(140,a,151,a)].
% 1.98/2.25 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(tc_nat,tc_bool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,tc_nat),B)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,tc_nat),C)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),B) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(140,a,157,a)].
% 1.98/2.25 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(140,a,158,a)].
% 1.98/2.25 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),A)). [resolve(140,a,159,a)].
% 1.98/2.25 Derived: c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,tc_nat),B),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C),tc_fun(tc_nat,tc_bool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,tc_nat),C) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(140,a,160,a)].
% 1.98/2.25 161 class_Orderings_Olinorder(tc_Int_Oint) # label(clsarity_Int__Oint__Orderings_Olinorder) # label(axiom). [assumption].
% 1.98/2.25 Derived: A = B | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),B)). [resolve(161,a,141,a)].
% 1.98/2.25 Derived: A = B | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),B),A)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),B)). [resolve(161,a,143,a)].
% 1.98/2.25 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),A)). [resolve(161,a,147,a)].
% 1.98/2.25 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),B)) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(161,a,148,a)].
% 1.98/2.25 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(161,a,151,a)].
% 1.98/2.25 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(tc_Int_Oint,tc_bool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,tc_Int_Oint),B)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,tc_Int_Oint),C)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_Int_Oint),B) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(161,a,157,a)].
% 1.98/2.25 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(161,a,158,a)].
% 1.98/2.25 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),B),A)). [resolve(161,a,159,a)].
% 1.98/2.25 Derived: c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,tc_Int_Oint),B),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_Int_Oint),C),tc_fun(tc_Int_Oint,tc_bool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(A,tc_Int_Oint),C) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(161,a,160,a)].
% 2.06/2.34 162 class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) # label(axiom). [assumption].
% 2.06/2.34 163 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B))) # label(cls_zero__less__double__add__iff__zero__less__single__add_0) # label(axiom). [assumption].
% 2.06/2.34 164 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_zero__less__double__add__iff__zero__less__single__add_1) # label(axiom). [assumption].
% 2.06/2.34 165 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),D) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) # label(axiom). [assumption].
% 2.06/2.34 166 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) # label(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) # label(axiom). [assumption].
% 2.06/2.34 167 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__less__zero__iff__single__less__zero_1) # label(axiom). [assumption].
% 2.06/2.34 168 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B)),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__less__zero__iff__single__less__zero_0) # label(axiom). [assumption].
% 2.06/2.34 169 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Lattices_Oupper__semilattice__class_Osup(B,C,A)),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)) # label(cls_add__eq__inf__sup_0) # label(axiom). [assumption].
% 2.06/2.34 170 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B))) # label(cls_zero__le__double__add__iff__zero__le__single__add_0) # label(axiom). [assumption].
% 2.06/2.34 171 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__le__double__add__iff__zero__le__single__add_1) # label(axiom). [assumption].
% 2.06/2.34 172 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__le__zero__iff__single__add__le__zero_0) # label(axiom). [assumption].
% 2.06/2.34 173 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__le__zero__iff__single__add__le__zero_1) # label(axiom). [assumption].
% 2.06/2.34 174 -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].
% 2.06/2.34 175 -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].
% 2.06/2.34 176 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Lattices_Oupper__semilattice__class_Osup(C,D,A)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) # label(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0) # label(axiom). [assumption].
% 2.06/2.34 177 -class_OrderedGroup_Olordered__ab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Lattices_Oupper__semilattice__class_Osup(B,C,A)),D) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0) # label(axiom). [assumption].
% 2.06/2.34 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A))). [resolve(162,a,163,a)].
% 2.06/2.34 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(162,a,164,a)].
% 2.06/2.34 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint)),C) = c_Lattices_Olower__semilattice__class_Oinf(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(162,a,165,a)].
% 2.06/2.34 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_Int_Oint)) = c_Lattices_Olower__semilattice__class_Oinf(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). [resolve(162,a,166,a)].
% 2.06/2.34 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(162,a,167,a)].
% 2.06/2.34 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(162,a,168,a)].
% 2.06/2.34 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint)),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint)). [resolve(162,a,169,a)].
% 2.06/2.34 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A))). [resolve(162,a,170,a)].
% 2.06/2.34 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(162,a,171,a)].
% 2.06/2.34 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(162,a,172,a)].
% 2.06/2.34 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(162,a,173,a)].
% 2.15/2.42 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(162,a,174,a)].
% 2.15/2.42 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_Int_Oint)) = c_Lattices_Oupper__semilattice__class_Osup(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). [resolve(162,a,176,a)].
% 2.15/2.42 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint)),C) = c_Lattices_Oupper__semilattice__class_Osup(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(162,a,177,a)].
% 2.15/2.42 178 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 2.15/2.42 179 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),D)) # label(cls_power__le__imp__le__exp_0) # label(axiom). [assumption].
% 2.15/2.42 180 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),D)) # label(cls_power__increasing__iff_0) # label(axiom). [assumption].
% 2.15/2.42 181 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) # label(cls_power__increasing__iff_1) # label(axiom). [assumption].
% 2.15/2.42 182 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),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)))) # label(cls_zero__less__two_0) # label(axiom). [assumption].
% 2.15/2.42 183 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),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)))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) # label(cls_power__less__power__Suc_0) # label(axiom). [assumption].
% 2.15/2.42 184 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 2.15/2.42 185 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A)))) # label(cls_less__add__one_0) # label(axiom). [assumption].
% 2.15/2.42 186 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),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)))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) # label(cls_power__gt1__lemma_0) # label(axiom). [assumption].
% 2.15/2.42 187 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_power__Suc__less_0) # label(axiom). [assumption].
% 2.15/2.42 188 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) # label(cls_power__increasing_0) # label(axiom). [assumption].
% 2.15/2.42 189 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C))),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_power__Suc__less__one_0) # label(axiom). [assumption].
% 2.15/2.42 190 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D))) # label(cls_power__less__imp__less__base_0) # label(axiom). [assumption].
% 2.15/2.42 191 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__le__power_0) # label(axiom). [assumption].
% 2.15/2.42 192 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_one__le__power_0) # label(axiom). [assumption].
% 2.15/2.42 193 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),D),C)) # label(cls_power__strict__decreasing_0) # label(axiom). [assumption].
% 2.15/2.42 194 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) # label(cls_power__decreasing_0) # label(axiom). [assumption].
% 2.15/2.42 195 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_zero__less__power_0) # label(axiom). [assumption].
% 2.15/2.42 196 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__one__less__zero_0) # label(axiom). [assumption].
% 2.15/2.42 197 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oone__class_Oone(A))) # label(cls_zero__le__one_0) # label(axiom). [assumption].
% 2.15/2.42 198 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_power__mono_0) # label(axiom). [assumption].
% 2.15/2.42 199 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) # label(cls_one__less__power_0) # label(axiom). [assumption].
% 2.15/2.42 200 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_power__strict__mono_0) # label(axiom). [assumption].
% 2.15/2.42 201 -class_Ring__and__Field_Oordered__semidom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C) | B = D | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__eq__imp__eq__base_0) # label(axiom). [assumption].
% 2.15/2.42 202 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__one__le__zero_0) # label(axiom). [assumption].
% 2.15/2.42 203 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) # label(cls_power__gt1_0) # label(axiom). [assumption].
% 2.15/2.42 204 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Oone__class_Oone(A))) # label(cls_zero__less__one_0) # label(axiom). [assumption].
% 2.15/2.42 205 -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) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) | C = D # label(cls_power__inject__exp_0) # label(axiom). [assumption].
% 2.15/2.42 206 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),D)) # label(cls_power__less__imp__less__exp_0) # label(axiom). [assumption].
% 2.15/2.42 207 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),D)) # label(cls_power__strict__increasing_0) # label(axiom). [assumption].
% 2.15/2.42 208 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B)),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),D)) # label(cls_power__strict__increasing__iff_0) # label(axiom). [assumption].
% 2.15/2.42 209 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) # label(cls_power__strict__increasing__iff_1) # label(axiom). [assumption].
% 2.15/2.42 210 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Oone__class_Oone(A)),B)) # label(cls_less__1__mult_0) # label(axiom). [assumption].
% 2.15/2.42 211 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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)))) # label(cls_power2__less__imp__less_0) # label(axiom). [assumption].
% 2.15/2.42 212 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,D)),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),hAPP(c_Suc,D)))) # label(cls_power__le__imp__le__base_0) # label(axiom). [assumption].
% 2.15/2.42 213 -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 | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__inject__base_0) # label(axiom). [assumption].
% 2.15/2.42 214 -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 | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power2__eq__imp__eq_0) # label(axiom). [assumption].
% 2.15/2.42 215 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(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)),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)))) # label(cls_power2__le__imp__le_0) # label(axiom). [assumption].
% 2.15/2.42 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),A),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),C)). [resolve(178,a,179,a)].
% 2.15/2.42 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)). [resolve(178,a,181,a)].
% 2.15/2.42 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),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)))). [resolve(178,a,182,a)].
% 2.15/2.42 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),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)))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)). [resolve(178,a,183,a)].
% 2.15/2.42 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)). [resolve(178,a,184,a)].
% 2.15/2.42 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)))). [resolve(178,a,185,a)].
% 2.15/2.42 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),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)))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)). [resolve(178,a,186,a)].
% 2.15/2.42 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),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))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(178,a,187,a)].
% 2.15/2.42 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(178,a,188,a)].
% 2.15/2.42 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B))),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(178,a,189,a)].
% 2.15/2.42 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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(178,a,190,a)].
% 2.15/2.42 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(178,a,191,a)].
% 2.15/2.42 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(178,a,192,a)].
% 2.15/2.42 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),B)). [resolve(178,a,193,a)].
% 2.15/2.42 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)). [resolve(178,a,194,a)].
% 2.15/2.42 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(178,a,195,a)].
% 2.15/2.42 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(178,a,196,a)].
% 2.15/2.42 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat))). [resolve(178,a,197,a)].
% 2.15/2.42 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(178,a,198,a)].
% 2.15/2.42 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)). [resolve(178,a,199,a)].
% 2.15/2.42 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(178,a,200,a)].
% 2.15/2.42 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B) | A = C | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(178,a,201,a)].
% 2.15/2.43 Derived: -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(178,a,202,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B)))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)). [resolve(178,a,203,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))). [resolve(178,a,204,a)].
% 2.15/2.43 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)) | B = C. [resolve(178,a,205,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),C),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),C)). [resolve(178,a,206,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)). [resolve(178,a,207,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)). [resolve(178,a,210,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,C)),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),hAPP(c_Suc,C)))). [resolve(178,a,212,a)].
% 2.15/2.43 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 | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(178,a,213,a)].
% 2.15/2.43 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 | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(178,a,214,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(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)),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)))). [resolve(178,a,215,a)].
% 2.15/2.43 216 class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 2.15/2.43 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),A),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),C)). [resolve(216,a,179,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),A)). [resolve(216,a,181,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),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)))). [resolve(216,a,182,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),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)))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),A)). [resolve(216,a,183,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),B)). [resolve(216,a,184,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint)))). [resolve(216,a,185,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),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)))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),A)). [resolve(216,a,186,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(216,a,187,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(216,a,188,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Suc,B))),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(216,a,189,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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(216,a,190,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(216,a,191,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(216,a,192,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),B)). [resolve(216,a,193,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)). [resolve(216,a,194,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(216,a,195,a)].
% 2.15/2.43 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(216,a,196,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))). [resolve(216,a,197,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(216,a,198,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),A)). [resolve(216,a,199,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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),C),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(216,a,200,a)].
% 2.15/2.43 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B) | A = C | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(216,a,201,a)].
% 2.15/2.43 Derived: -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(216,a,202,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Suc,B)))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),A)). [resolve(216,a,203,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_HOL_Oone__class_Oone(tc_Int_Oint))). [resolve(216,a,204,a)].
% 2.15/2.43 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) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),A)) | B = C. [resolve(216,a,205,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),A)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),C)). [resolve(216,a,206,a)].
% 2.15/2.43 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)). [resolve(216,a,207,a)].
% 2.26/2.52 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),A)). [resolve(216,a,210,a)].
% 2.26/2.52 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Suc,C)),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),hAPP(c_Suc,C)))). [resolve(216,a,212,a)].
% 2.26/2.52 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 | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(216,a,213,a)].
% 2.26/2.52 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 | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(216,a,214,a)].
% 2.26/2.52 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(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)),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)))). [resolve(216,a,215,a)].
% 2.26/2.52 217 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 2.26/2.52 218 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 2.26/2.52 219 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 2.26/2.52 220 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_le__infI_0) # label(axiom). [assumption].
% 2.26/2.52 221 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A),C)) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 2.26/2.52 222 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A),B)) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 2.26/2.52 223 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) # label(cls_less__infI2_0) # label(axiom). [assumption].
% 2.26/2.52 224 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_less__infI1_0) # label(axiom). [assumption].
% 2.26/2.52 225 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A) # label(cls_inf__left__commute_0) # label(axiom). [assumption].
% 2.26/2.52 226 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_inf__assoc_0) # label(axiom). [assumption].
% 2.26/2.52 227 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) # label(cls_le__infE_0) # label(axiom). [assumption].
% 2.26/2.52 228 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Olower__semilattice__class_Oinf(D,C,A))) # label(cls_le__infE_1) # label(axiom). [assumption].
% 2.26/2.52 229 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A),D)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 2.26/2.52 230 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A),D)) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 2.26/2.52 231 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 2.26/2.52 232 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Olower__semilattice__class_Oinf(D,C,A))) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 2.26/2.52 233 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = C | -hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 2.26/2.52 234 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) != B | hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 2.26/2.52 235 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = B | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 2.26/2.52 236 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = c_Lattices_Olower__semilattice__class_Oinf(C,B,A) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 2.26/2.52 237 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A) = c_Lattices_Olower__semilattice__class_Oinf(B,C,A) # label(cls_inf__left__idem_0) # label(axiom). [assumption].
% 2.26/2.52 238 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 2.26/2.52 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),c_Lattices_Olower__semilattice__class_Oinf(D,E,tc_fun(C,A)))) | -hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),E)) | -hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),D)). [resolve(217,a,218,a)].
% 2.26/2.52 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)),C)). [resolve(217,a,221,a)].
% 2.26/2.52 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)),B)). [resolve(217,a,222,a)].
% 2.26/2.52 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,A))),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),D),E)). [resolve(217,a,223,a)].
% 2.26/2.52 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,A))),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),C),E)). [resolve(217,a,224,a)].
% 2.26/2.52 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,tc_fun(E,A)),tc_fun(E,A)). [resolve(217,a,225,a)].
% 2.26/2.52 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(217,a,226,a)].
% 2.26/2.52 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),D)) | -hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),c_Lattices_Olower__semilattice__class_Oinf(D,E,tc_fun(C,A)))). [resolve(217,a,227,a)].
% 2.26/2.52 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),D)) | -hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),c_Lattices_Olower__semilattice__class_Oinf(E,D,tc_fun(C,A)))). [resolve(217,a,228,a)].
% 2.26/2.52 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)),E)) | -hBOOL(hAPP(c_lessequals(B,tc_fun(D,A)),E)). [resolve(217,a,229,a)].
% 2.26/2.52 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)),E)) | -hBOOL(hAPP(c_lessequals(C,tc_fun(D,A)),E)). [resolve(217,a,230,a)].
% 2.26/2.52 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = C | -hBOOL(hAPP(c_lessequals(C,tc_fun(D,A)),B)). [resolve(217,a,233,a)].
% 2.26/2.52 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) != B | hBOOL(hAPP(c_lessequals(B,tc_fun(D,A)),C)). [resolve(217,a,234,a)].
% 2.26/2.52 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = B | -hBOOL(hAPP(c_lessequals(B,tc_fun(D,A)),C)). [resolve(217,a,235,a)].
% 2.26/2.52 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_fun(D,A)). [resolve(217,a,236,a)].
% 2.26/2.52 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)). [resolve(217,a,237,a)].
% 2.26/2.52 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(217,a,238,a)].
% 2.26/2.52 239 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 2.26/2.52 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(239,a,218,a)].
% 2.26/2.52 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat),B)). [resolve(239,a,221,a)].
% 2.26/2.52 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat),A)). [resolve(239,a,222,a)].
% 2.26/2.52 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)). [resolve(239,a,223,a)].
% 2.26/2.52 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(239,a,224,a)].
% 2.26/2.52 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_nat),tc_nat). [resolve(239,a,225,a)].
% 2.26/2.52 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat). [resolve(239,a,226,a)].
% 2.26/2.52 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat))). [resolve(239,a,227,a)].
% 2.26/2.52 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_nat))). [resolve(239,a,228,a)].
% 2.26/2.52 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(239,a,229,a)].
% 2.26/2.52 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(239,a,230,a)].
% 2.26/2.52 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = B | -hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(239,a,233,a)].
% 2.26/2.52 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) != A | hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(239,a,234,a)].
% 2.26/2.52 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = A | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(239,a,235,a)].
% 2.26/2.52 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_nat). [resolve(239,a,236,a)].
% 2.26/2.52 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat). [resolve(239,a,237,a)].
% 2.26/2.52 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_nat) = A. [resolve(239,a,238,a)].
% 2.26/2.52 240 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 2.26/2.52 Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool))) | -hBOOL(hAPP(c_lessequals(A,tc_bool),C)) | -hBOOL(hAPP(c_lessequals(A,tc_bool),B)). [resolve(240,a,218,a)].
% 2.26/2.52 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool),B)). [resolve(240,a,221,a)].
% 2.26/2.52 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool),A)). [resolve(240,a,222,a)].
% 2.26/2.52 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),B),C)). [resolve(240,a,223,a)].
% 2.26/2.52 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),C)). [resolve(240,a,224,a)].
% 2.26/2.52 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_bool),tc_bool). [resolve(240,a,225,a)].
% 2.26/2.52 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(240,a,226,a)].
% 2.26/2.52 Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),B)) | -hBOOL(hAPP(c_lessequals(A,tc_bool),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool))). [resolve(240,a,227,a)].
% 2.26/2.52 Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),B)) | -hBOOL(hAPP(c_lessequals(A,tc_bool),c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_bool))). [resolve(240,a,228,a)].
% 2.26/2.52 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool),C)) | -hBOOL(hAPP(c_lessequals(A,tc_bool),C)). [resolve(240,a,229,a)].
% 2.26/2.52 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool),C)) | -hBOOL(hAPP(c_lessequals(B,tc_bool),C)). [resolve(240,a,230,a)].
% 2.26/2.52 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -hBOOL(hAPP(c_lessequals(B,tc_bool),A)). [resolve(240,a,233,a)].
% 2.26/2.52 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | hBOOL(hAPP(c_lessequals(A,tc_bool),B)). [resolve(240,a,234,a)].
% 2.26/2.52 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -hBOOL(hAPP(c_lessequals(A,tc_bool),B)). [resolve(240,a,235,a)].
% 2.36/2.61 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(240,a,236,a)].
% 2.36/2.61 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool). [resolve(240,a,237,a)].
% 2.36/2.61 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(240,a,238,a)].
% 2.36/2.61 241 class_Lattices_Olower__semilattice(tc_Int_Oint) # label(clsarity_Int__Oint__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 2.36/2.61 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(241,a,218,a)].
% 2.36/2.61 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),tc_Int_Oint),B)). [resolve(241,a,221,a)].
% 2.36/2.61 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),tc_Int_Oint),A)). [resolve(241,a,222,a)].
% 2.36/2.61 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),B),C)). [resolve(241,a,223,a)].
% 2.36/2.61 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(241,a,224,a)].
% 2.36/2.61 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_Int_Oint),tc_Int_Oint) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(241,a,225,a)].
% 2.36/2.61 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(241,a,226,a)].
% 2.36/2.61 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_Int_Oint))). [resolve(241,a,227,a)].
% 2.36/2.61 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_Int_Oint))). [resolve(241,a,228,a)].
% 2.36/2.61 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(241,a,229,a)].
% 2.36/2.61 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),C)). [resolve(241,a,230,a)].
% 2.36/2.61 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint) = B | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(241,a,233,a)].
% 2.36/2.61 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint) != A | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(241,a,234,a)].
% 2.36/2.61 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint) = A | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(241,a,235,a)].
% 2.36/2.61 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_Int_Oint). [resolve(241,a,236,a)].
% 2.36/2.61 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),tc_Int_Oint) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint). [resolve(241,a,237,a)].
% 2.36/2.61 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_Int_Oint) = A. [resolve(241,a,238,a)].
% 2.36/2.61 242 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 2.36/2.61 243 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(A) # label(cls_class__semiring_Opwr__0_0) # label(axiom). [assumption].
% 2.36/2.61 244 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E)) # label(cls_class__semiring_Osemiring__rules_I20_J_0) # label(axiom). [assumption].
% 2.36/2.61 245 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) # label(cls_class__semiring_Omul__pwr_0) # label(axiom). [assumption].
% 2.36/2.61 246 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Oadd__a_0) # label(axiom). [assumption].
% 2.36/2.61 247 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Osemiring__rules_I24_J_0) # label(axiom). [assumption].
% 2.36/2.61 248 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Oadd__c_0) # label(axiom). [assumption].
% 2.36/2.61 249 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A))),B) # label(cls_class__semiring_Osemiring__rules_I4_J_0) # label(axiom). [assumption].
% 2.36/2.61 250 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Oone__class_Oone(tc_nat)) = B # label(cls_class__semiring_Osemiring__rules_I33_J_0) # label(axiom). [assumption].
% 2.36/2.62 251 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A))),C) # label(cls_class__semiring_Osemiring__rules_I2_J_0) # label(axiom). [assumption].
% 2.36/2.62 252 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),c_HOL_Oone__class_Oone(A))),B) # label(cls_class__semiring_Osemiring__rules_I3_J_0) # label(axiom). [assumption].
% 2.36/2.62 253 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Osemiring__rules_I25_J_0) # label(axiom). [assumption].
% 2.36/2.62 254 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I23_J_0) # label(axiom). [assumption].
% 2.36/2.62 255 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I22_J_0) # label(axiom). [assumption].
% 2.36/2.62 256 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I21_J_0) # label(axiom). [assumption].
% 2.36/2.62 257 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(A),c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A) # label(cls_class__semiring_Ogb__semiring__axioms_H_0) # label(axiom). [assumption].
% 2.36/2.62 258 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Oadd__0_0) # label(axiom). [assumption].
% 2.36/2.62 259 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_class__semiring_Osemiring__rules_I6_J_0) # label(axiom). [assumption].
% 2.36/2.62 260 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Osemiring__rules_I5_J_0) # label(axiom). [assumption].
% 2.36/2.62 261 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I1_J_0) # label(axiom). [assumption].
% 2.36/2.62 262 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_class__semiring_Omul__d_0) # label(axiom). [assumption].
% 2.36/2.62 263 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I8_J_0) # label(axiom). [assumption].
% 2.36/2.62 264 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D)) # label(cls_class__semiring_Opwr__mul_0) # label(axiom). [assumption].
% 2.36/2.62 265 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_class__semiring_Omul__1_0) # label(axiom). [assumption].
% 2.36/2.62 266 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oone__class_Oone(A)) = B # label(cls_class__semiring_Osemiring__rules_I12_J_0) # label(axiom). [assumption].
% 2.36/2.62 267 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B) = B # label(cls_class__semiring_Osemiring__rules_I11_J_0) # label(axiom). [assumption].
% 2.36/2.62 268 -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].
% 2.36/2.62 269 -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].
% 2.36/2.62 270 -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].
% 2.36/2.62 271 -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].
% 2.36/2.62 272 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),D) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) # label(cls_class__semiring_Opwr__pwr_0) # label(axiom). [assumption].
% 2.36/2.62 273 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),B) = hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) # label(cls_class__semiring_Osemiring__rules_I29_J_0) # label(axiom). [assumption].
% 2.36/2.62 274 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)) # label(cls_class__semiring_Osemiring__rules_I36_J_0) # label(axiom). [assumption].
% 2.36/2.62 275 -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].
% 2.36/2.62 276 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Omul__0_0) # label(axiom). [assumption].
% 2.36/2.62 277 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A)) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I10_J_0) # label(axiom). [assumption].
% 2.36/2.62 278 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__semiring_Osemiring__rules_I9_J_0) # label(axiom). [assumption].
% 2.36/2.62 279 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) # label(cls_class__semiring_Omul__a_0) # label(axiom). [assumption].
% 2.36/2.62 280 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I19_J_0) # label(axiom). [assumption].
% 2.36/2.62 281 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) # label(cls_class__semiring_Osemiring__rules_I18_J_0) # label(axiom). [assumption].
% 2.36/2.62 282 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I17_J_0) # label(axiom). [assumption].
% 2.36/2.62 283 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I16_J_0) # label(axiom). [assumption].
% 2.36/2.62 284 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),E)) # label(cls_class__semiring_Osemiring__rules_I15_J_0) # label(axiom). [assumption].
% 2.36/2.62 285 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) # label(cls_class__semiring_Osemiring__rules_I14_J_0) # label(axiom). [assumption].
% 2.36/2.62 286 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) # label(cls_class__semiring_Osemiring__rules_I13_J_0) # label(axiom). [assumption].
% 2.36/2.62 287 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B) # label(cls_class__semiring_Omul__c_0) # label(axiom). [assumption].
% 2.36/2.62 288 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B) # label(cls_class__semiring_Osemiring__rules_I7_J_0) # label(axiom). [assumption].
% 2.36/2.62 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(242,a,243,a)].
% 2.36/2.62 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(242,a,244,a)].
% 2.36/2.62 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(242,a,245,a)].
% 2.36/2.62 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(242,a,246,a)].
% 2.36/2.62 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(242,a,249,a)].
% 2.36/2.62 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(242,a,250,a)].
% 2.36/2.62 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(242,a,251,a)].
% 2.36/2.62 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(242,a,252,a)].
% 2.36/2.62 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(242,a,254,a)].
% 2.36/2.62 Derived: c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(tc_nat),c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(242,a,257,a)].
% 2.36/2.62 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(242,a,261,a)].
% 2.36/2.62 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(242,a,262,a)].
% 2.36/2.62 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(242,a,263,a)].
% 2.36/2.62 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(242,a,264,a)].
% 2.36/2.62 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = A. [resolve(242,a,265,a)].
% 2.36/2.62 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(242,a,266,a)].
% 2.36/2.62 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(242,a,268,a)].
% 2.36/2.62 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(242,a,270,a)].
% 2.36/2.62 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(242,a,271,a)].
% 2.36/2.62 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(242,a,272,a)].
% 2.36/2.62 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(242,a,273,a)].
% 2.36/2.62 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(242,a,274,a)].
% 2.36/2.62 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(242,a,275,a)].
% 2.36/2.62 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(242,a,276,a)].
% 2.36/2.62 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(242,a,277,a)].
% 2.36/2.62 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(242,a,279,a)].
% 2.36/2.62 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(242,a,280,a)].
% 2.36/2.62 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(242,a,282,a)].
% 2.36/2.62 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(242,a,283,a)].
% 2.36/2.62 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(242,a,286,a)].
% 2.36/2.62 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(242,a,287,a)].
% 2.36/2.62 289 class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 2.36/2.62 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(289,a,243,a)].
% 2.36/2.62 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(289,a,244,a)].
% 2.36/2.62 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(289,a,245,a)].
% 2.36/2.62 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(289,a,246,a)].
% 2.36/2.62 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(289,a,249,a)].
% 2.36/2.62 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(289,a,250,a)].
% 2.36/2.62 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(289,a,251,a)].
% 2.36/2.62 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(289,a,252,a)].
% 2.36/2.62 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(289,a,254,a)].
% 2.36/2.62 Derived: c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(289,a,257,a)].
% 2.36/2.62 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(289,a,261,a)].
% 2.36/2.62 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(289,a,262,a)].
% 2.36/2.62 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(289,a,263,a)].
% 2.36/2.62 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(289,a,264,a)].
% 2.36/2.62 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),A) = A. [resolve(289,a,265,a)].
% 2.36/2.62 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(289,a,266,a)].
% 2.36/2.62 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(289,a,268,a)].
% 2.36/2.62 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(289,a,270,a)].
% 2.36/2.62 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(289,a,271,a)].
% 2.36/2.62 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(289,a,272,a)].
% 2.36/2.62 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(289,a,273,a)].
% 2.36/2.62 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(289,a,274,a)].
% 2.36/2.62 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(289,a,275,a)].
% 2.36/2.62 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(289,a,276,a)].
% 2.36/2.62 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(289,a,277,a)].
% 2.36/2.62 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(289,a,279,a)].
% 2.36/2.62 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(289,a,280,a)].
% 2.36/2.62 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(289,a,282,a)].
% 2.36/2.62 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(289,a,283,a)].
% 2.36/2.62 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(289,a,286,a)].
% 2.45/2.72 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(289,a,287,a)].
% 2.45/2.72 290 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 2.45/2.72 291 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,C)),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C),D))),B) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) # label(cls_lemma__realpow__diff_0) # label(axiom). [assumption].
% 2.45/2.72 292 -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].
% 2.45/2.72 293 -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].
% 2.45/2.72 294 -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].
% 2.45/2.72 295 -class_Ring__and__Field_Oordered__ring__strict(A) | -class_OrderedGroup_Omonoid__mult(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__even__power_0) # label(axiom). [assumption].
% 2.45/2.72 296 -class_Ring__and__Field_Ocomm__ring(A) | -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(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))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),D)),hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),hAPP(c_Power_Opower__class_Opower(A),B)),tc_nat,A,A),hAPP(hAPP(c_COMBB(tc_nat,A,tc_nat),hAPP(c_Power_Opower__class_Opower(A),D)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C))),tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,C)))) # label(cls_lemma__realpow__diff__sumr2_0) # label(axiom). [assumption].
% 2.45/2.72 297 -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].
% 2.45/2.72 298 -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].
% 2.45/2.72 299 -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].
% 2.45/2.72 300 -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].
% 2.45/2.72 301 -class_Ring__and__Field_Ocomm__semiring__0(A) | -class_OrderedGroup_Omonoid__mult(A) | hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),hAPP(c_Power_Opower__class_Opower(A),B)),tc_nat,A,A),hAPP(hAPP(c_COMBB(tc_nat,A,tc_nat),hAPP(c_Power_Opower__class_Opower(A),C)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,D)))),tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,D))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),hAPP(c_Power_Opower__class_Opower(A),B)),tc_nat,A,A),hAPP(hAPP(c_COMBB(tc_nat,A,tc_nat),hAPP(c_Power_Opower__class_Opower(A),C)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D))),tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,D)))) # label(cls_lemma__realpow__diff__sumr_0) # label(axiom). [assumption].
% 2.45/2.72 302 -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].
% 2.45/2.72 303 -class_Ring__and__Field_Ocomm__ring(A) | -class_OrderedGroup_Omonoid__mult(A) | hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Ominus__class_Ominus(A)),hAPP(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),hAPP(hAPP(c_COMBB(tc_nat,A,tc_nat),hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D))),tc_nat,A,A),hAPP(c_Power_Opower__class_Opower(A),B))),tc_nat,A,A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D)),tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),D)) = hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Otimes__class_Otimes(A)),hAPP(c_Power_Opower__class_Opower(A),B)),tc_nat,A,A),hAPP(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),tc_nat),c_HOL_Ominus__class_Ominus(A)),hAPP(hAPP(c_COMBB(tc_nat,A,tc_nat),hAPP(c_Power_Opower__class_Opower(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D))),tc_nat,A,A),hAPP(hAPP(c_COMBB(tc_nat,A,tc_nat),hAPP(c_Power_Opower__class_Opower(A),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),D)))),tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),D)) # label(cls_lemma__termdiff1_0) # label(axiom). [assumption].
% 2.45/2.72 304 -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].
% 2.45/2.72 305 -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].
% 2.45/2.72 306 -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].
% 2.45/2.72 307 -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].
% 2.45/2.72 308 -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].
% 2.45/2.72 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,B)),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C))),A) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)). [resolve(290,a,291,a)].
% 2.45/2.72 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(290,a,292,a)].
% 2.45/2.72 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(290,a,294,a)].
% 2.45/2.72 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_nat) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B))) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(290,a,295,b)].
% 2.45/2.72 Derived: -class_Ring__and__Field_Ocomm__ring(tc_nat) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),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))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),A),C)),hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(tc_nat)),hAPP(c_Power_Opower__class_Opower(tc_nat),A)),tc_nat,tc_nat,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_nat,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),C)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B))),tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,B)))). [resolve(290,a,296,b)].
% 2.45/2.72 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(290,a,300,a)].
% 2.45/2.72 Derived: -class_Ring__and__Field_Ocomm__semiring__0(tc_nat) | hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(tc_nat)),hAPP(c_Power_Opower__class_Opower(tc_nat),A)),tc_nat,tc_nat,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_nat,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,C)))),tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,C))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(tc_nat)),hAPP(c_Power_Opower__class_Opower(tc_nat),A)),tc_nat,tc_nat,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_nat,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C))),tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,C)))). [resolve(290,a,301,b)].
% 2.45/2.72 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(290,a,302,a)].
% 2.45/2.72 Derived: -class_Ring__and__Field_Ocomm__ring(tc_nat) | hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(tc_nat)),hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(tc_nat)),hAPP(hAPP(c_COMBB(tc_nat,tc_nat,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C))),tc_nat,tc_nat,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),A))),tc_nat,tc_nat,tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C)),tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) = hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(tc_nat)),hAPP(c_Power_Opower__class_Opower(tc_nat),A)),tc_nat,tc_nat,tc_nat),hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(tc_nat)),hAPP(hAPP(c_COMBB(tc_nat,tc_nat,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C))),tc_nat,tc_nat,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_nat,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_nat),A)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C)))),tc_nat,tc_nat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)). [resolve(290,a,303,b)].
% 2.45/2.72 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(290,a,304,a)].
% 2.45/2.72 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(290,a,305,a)].
% 2.45/2.72 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(290,a,306,a)].
% 2.45/2.72 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(290,a,308,a)].
% 2.45/2.72 309 class_OrderedGroup_Omonoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 2.45/2.72 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,B)),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B),C))),A) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)). [resolve(309,a,291,a)].
% 2.45/2.72 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(309,a,292,a)].
% 2.45/2.72 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(309,a,294,a)].
% 2.45/2.72 Derived: -class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),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(309,a,295,b)].
% 2.45/2.72 Derived: -class_Ring__and__Field_Ocomm__ring(tc_Int_Oint) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),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))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),C)),hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),c_HOL_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A)),tc_nat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_nat,tc_Int_Oint,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),C)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),B))),tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,B)))). [resolve(309,a,296,b)].
% 2.45/2.72 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(309,a,300,a)].
% 2.45/2.72 Derived: -class_Ring__and__Field_Ocomm__semiring__0(tc_Int_Oint) | hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),c_HOL_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A)),tc_nat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_nat,tc_Int_Oint,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),hAPP(c_Suc,C)))),tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,C))) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),c_HOL_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A)),tc_nat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_nat,tc_Int_Oint,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C))),tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(c_Suc,C)))). [resolve(309,a,301,b)].
% 2.45/2.72 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(309,a,302,a)].
% 2.45/2.72 Derived: -class_Ring__and__Field_Ocomm__ring(tc_Int_Oint) | hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),c_HOL_Ominus__class_Ominus(tc_Int_Oint)),hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),c_HOL_Otimes__class_Otimes(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_nat,tc_Int_Oint,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C))),tc_nat,tc_Int_Oint,tc_Int_Oint),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A))),tc_nat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C)),tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) = hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),c_HOL_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A)),tc_nat,tc_Int_Oint,tc_Int_Oint),hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_nat),c_HOL_Ominus__class_Ominus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_nat,tc_Int_Oint,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B))),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C))),tc_nat,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_nat,tc_Int_Oint,tc_nat),hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A)),hAPP(c_HOL_Ominus__class_Ominus(tc_nat),C)))),tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)). [resolve(309,a,303,b)].
% 2.45/2.72 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(309,a,304,a)].
% 2.45/2.72 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(309,a,305,a)].
% 2.45/2.72 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(309,a,306,a)].
% 2.58/2.90 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(309,a,308,a)].
% 2.58/2.90 310 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 2.58/2.90 311 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 2.58/2.90 312 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 2.58/2.90 313 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__mono_0) # label(axiom). [assumption].
% 2.58/2.90 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(310,a,311,a)].
% 2.58/2.90 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(310,a,312,a)].
% 2.58/2.90 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(310,a,313,a)].
% 2.58/2.90 314 class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 2.58/2.90 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(314,a,311,a)].
% 2.58/2.90 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),C)). [resolve(314,a,312,a)].
% 2.58/2.90 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(314,a,313,a)].
% 2.58/2.90 315 class_OrderedGroup_Oab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 2.58/2.90 316 -class_OrderedGroup_Oab__group__add(A) | hAPP(c_Finite__Set_Osetsum(B,C,A),c_Lattices_Oupper__semilattice__class_Osup(D,E,tc_fun(C,tc_bool))) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(c_Finite__Set_Osetsum(B,C,A),D)),hAPP(c_Finite__Set_Osetsum(B,C,A),E))),hAPP(c_Finite__Set_Osetsum(B,C,A),c_Lattices_Olower__semilattice__class_Oinf(D,E,tc_fun(C,tc_bool)))) | -c_Finite__Set_Ofinite(E,C) | -c_Finite__Set_Ofinite(D,C) # label(cls_setsum__Un_0) # label(axiom). [assumption].
% 2.58/2.90 317 -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].
% 2.58/2.90 318 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),D))),hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(C,tc_nat),E))) = hAPP(c_Finite__Set_Osetsum(B,tc_nat,A),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(E,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(E,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(C,tc_nat),E)) # label(cls_setsum__diff__nat__ivl_0) # label(axiom). [assumption].
% 2.58/2.90 319 -class_OrderedGroup_Oab__group__add(A) | hAPP(c_Finite__Set_Osetsum(B,C,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(C,tc_bool)),D),c_Set_Oinsert(E,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C))) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_Finite__Set_Osetsum(B,C,A),D)),hAPP(B,E)) | -hBOOL(hAPP(hAPP(c_in(C),E),D)) | -c_Finite__Set_Ofinite(D,C) # label(cls_setsum__diff1_0) # label(axiom). [assumption].
% 2.58/2.90 320 -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].
% 2.58/2.90 321 -class_OrderedGroup_Oab__group__add(A) | hAPP(c_Finite__Set_Osetsum(B,C,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(C,tc_bool)),D),c_Set_Oinsert(E,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C))) = hAPP(c_Finite__Set_Osetsum(B,C,A),D) | hBOOL(hAPP(hAPP(c_in(C),E),D)) | -c_Finite__Set_Ofinite(D,C) # label(cls_setsum__diff1_1) # label(axiom). [assumption].
% 2.58/2.90 322 -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].
% 2.58/2.90 323 -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].
% 2.58/2.90 324 -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].
% 2.58/2.90 325 -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].
% 2.58/2.90 326 -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].
% 2.58/2.90 327 -class_OrderedGroup_Oab__group__add(A) | hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Ominus__class_Ominus(A)),C),B,A,A),D),B,A),E) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_Finite__Set_Osetsum(C,B,A),E)),hAPP(c_Finite__Set_Osetsum(D,B,A),E)) # label(cls_setsum__subtractf_0) # label(axiom). [assumption].
% 2.58/2.90 Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(B,tc_bool))) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),C)),hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),D))),hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,tc_bool)))) | -c_Finite__Set_Ofinite(D,B) | -c_Finite__Set_Ofinite(C,B). [resolve(315,a,316,a)].
% 2.58/2.90 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(315,a,317,a)].
% 2.83/3.08 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),C))),hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(B,tc_nat),D))) = hAPP(c_Finite__Set_Osetsum(A,tc_nat,tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(D,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)). [resolve(315,a,318,a)].
% 2.83/3.08 Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(B,tc_bool)),C),c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B))) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),C)),hAPP(A,D)) | -hBOOL(hAPP(hAPP(c_in(B),D),C)) | -c_Finite__Set_Ofinite(C,B). [resolve(315,a,319,a)].
% 2.83/3.08 Derived: hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(B,tc_bool)),C),c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B))) = hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),C) | hBOOL(hAPP(hAPP(c_in(B),D),C)) | -c_Finite__Set_Ofinite(C,B). [resolve(315,a,321,a)].
% 2.83/3.08 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(315,a,322,a)].
% 2.83/3.08 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(315,a,323,a)].
% 2.83/3.08 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(315,a,324,a)].
% 2.83/3.08 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),A) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(315,a,325,a)].
% 2.83/3.08 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = B. [resolve(315,a,326,a)].
% 2.83/3.08 Derived: hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),A),c_HOL_Ominus__class_Ominus(tc_Int_Oint)),B),A,tc_Int_Oint,tc_Int_Oint),C),A,tc_Int_Oint),D) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Finite__Set_Osetsum(B,A,tc_Int_Oint),D)),hAPP(c_Finite__Set_Osetsum(C,A,tc_Int_Oint),D)). [resolve(315,a,327,a)].
% 2.83/3.08 328 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 2.83/3.08 329 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__nonpos__neg_0) # label(axiom). [assumption].
% 2.83/3.08 330 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__nonpos_0) # label(axiom). [assumption].
% 2.83/3.08 331 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__nonneg__pos_0) # label(axiom). [assumption].
% 2.83/3.08 332 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_add__pos__nonneg_0) # label(axiom). [assumption].
% 2.84/3.08 333 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__nonneg__nonneg_0) # label(axiom). [assumption].
% 2.84/3.08 334 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_1) # label(axiom). [assumption].
% 2.84/3.08 335 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_0) # label(axiom). [assumption].
% 2.84/3.08 336 -class_OrderedGroup_Opordered__comm__monoid__add(A) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(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].
% 2.84/3.08 337 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 2.84/3.08 338 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 2.84/3.08 339 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__nonpos__nonpos_0) # label(axiom). [assumption].
% 2.84/3.08 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(328,a,329,a)].
% 2.84/3.08 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(328,a,330,a)].
% 2.84/3.08 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(328,a,331,a)].
% 2.84/3.08 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(328,a,332,a)].
% 2.84/3.08 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(328,a,333,a)].
% 2.84/3.08 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(328,a,334,a)].
% 2.84/3.08 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(328,a,335,a)].
% 2.84/3.08 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(328,a,338,a)].
% 2.84/3.08 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(328,a,339,a)].
% 2.84/3.08 340 class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 2.84/3.08 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(340,a,329,a)].
% 2.84/3.08 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(340,a,330,a)].
% 2.84/3.08 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(340,a,331,a)].
% 2.84/3.08 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(340,a,332,a)].
% 2.84/3.08 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(340,a,333,a)].
% 2.84/3.08 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(340,a,334,a)].
% 2.84/3.08 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(340,a,335,a)].
% 2.88/3.19 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(340,a,338,a)].
% 2.88/3.19 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(340,a,339,a)].
% 2.88/3.19 341 c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(tc_nat),c_Power_Opower__class_Opower(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(242,a,257,a)].
% 2.88/3.19 342 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),hAPP(hAPP(B,E),D)) = hAPP(hAPP(B,hAPP(hAPP(A,C),E)),D) | -c_Groebner__Basis_Ogb__semiring(A,B,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I1_J_0) # label(axiom). [assumption].
% 2.88/3.19 343 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),D) = hAPP(hAPP(B,hAPP(hAPP(A,C),E)),D) | -c_Groebner__Basis_Ogb__semiring(A,B,F,V6,E,V7) # label(cls_gb__semiring_Osemiring__rules_I2_J_0) # label(axiom). [assumption].
% 2.88/3.19 344 hAPP(hAPP(A,B),hAPP(hAPP(C,D),B)) = hAPP(hAPP(C,hAPP(hAPP(A,D),E)),B) | -c_Groebner__Basis_Ogb__semiring(A,C,F,V6,E,V7) # label(cls_gb__semiring_Osemiring__rules_I3_J_0) # label(axiom). [assumption].
% 2.88/3.19 345 hAPP(hAPP(A,B),B) = hAPP(hAPP(C,hAPP(hAPP(A,D),D)),B) | -c_Groebner__Basis_Ogb__semiring(A,C,E,F,D,V6) # label(cls_gb__semiring_Osemiring__rules_I4_J_0) # label(axiom). [assumption].
% 2.88/3.19 346 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(A,D,E,B,F,V6) # label(cls_gb__semiring_Osemiring__rules_I5_J_0) # label(axiom). [assumption].
% 2.88/3.19 347 hAPP(hAPP(A,B),C) = B | -c_Groebner__Basis_Ogb__semiring(A,D,E,C,F,V6) # label(cls_gb__semiring_Osemiring__rules_I6_J_0) # label(axiom). [assumption].
% 2.88/3.19 348 hAPP(hAPP(A,B),C) = hAPP(hAPP(A,C),B) | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I7_J_0) # label(axiom). [assumption].
% 2.88/3.19 349 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),E) = hAPP(hAPP(B,hAPP(hAPP(A,C),E)),hAPP(hAPP(A,D),E)) | -c_Groebner__Basis_Ogb__semiring(B,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I8_J_0) # label(axiom). [assumption].
% 2.88/3.19 350 hAPP(hAPP(A,B),C) = B | -c_Groebner__Basis_Ogb__semiring(D,A,E,B,F,V6) # label(cls_gb__semiring_Osemiring__rules_I9_J_0) # label(axiom). [assumption].
% 2.88/3.19 351 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(D,A,E,C,F,V6) # label(cls_gb__semiring_Osemiring__rules_I10_J_0) # label(axiom). [assumption].
% 2.88/3.19 352 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,B,V6) # label(cls_gb__semiring_Osemiring__rules_I11_J_0) # label(axiom). [assumption].
% 2.88/3.19 353 hAPP(hAPP(A,B),C) = B | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,C,V6) # label(cls_gb__semiring_Osemiring__rules_I12_J_0) # label(axiom). [assumption].
% 2.88/3.19 354 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E)) = hAPP(hAPP(A,hAPP(hAPP(A,B),D)),hAPP(hAPP(A,C),E)) | -c_Groebner__Basis_Ogb__semiring(F,A,V6,V7,V8,V9) # label(cls_gb__semiring_Osemiring__rules_I13_J_0) # label(axiom). [assumption].
% 2.88/3.19 355 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E)) = hAPP(hAPP(A,B),hAPP(hAPP(A,C),hAPP(hAPP(A,D),E))) | -c_Groebner__Basis_Ogb__semiring(F,A,V6,V7,V8,V9) # label(cls_gb__semiring_Osemiring__rules_I14_J_0) # label(axiom). [assumption].
% 2.88/3.19 356 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E)) = hAPP(hAPP(A,D),hAPP(hAPP(A,hAPP(hAPP(A,B),C)),E)) | -c_Groebner__Basis_Ogb__semiring(F,A,V6,V7,V8,V9) # label(cls_gb__semiring_Osemiring__rules_I15_J_0) # label(axiom). [assumption].
% 2.88/3.19 357 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,hAPP(hAPP(A,B),D)),C) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I16_J_0) # label(axiom). [assumption].
% 2.88/3.19 358 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I17_J_0) # label(axiom). [assumption].
% 2.88/3.19 359 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I18_J_0) # label(axiom). [assumption].
% 2.88/3.19 360 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,C),hAPP(hAPP(A,B),D)) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I19_J_0) # label(axiom). [assumption].
% 2.88/3.19 361 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,D),E)) = hAPP(hAPP(A,hAPP(hAPP(A,B),D)),hAPP(hAPP(A,C),E)) | -c_Groebner__Basis_Ogb__semiring(A,F,V6,V7,V8,V9) # label(cls_gb__semiring_Osemiring__rules_I20_J_0) # label(axiom). [assumption].
% 2.88/3.19 362 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I21_J_0) # label(axiom). [assumption].
% 2.88/3.19 363 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,C),hAPP(hAPP(A,B),D)) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I22_J_0) # label(axiom). [assumption].
% 2.88/3.19 364 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,hAPP(hAPP(A,B),D)),C) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I23_J_0) # label(axiom). [assumption].
% 2.88/3.19 365 hAPP(hAPP(A,B),C) = hAPP(hAPP(A,C),B) | -c_Groebner__Basis_Ogb__semiring(A,D,E,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I24_J_0) # label(axiom). [assumption].
% 2.88/3.19 366 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Osemiring__rules_I25_J_0) # label(axiom). [assumption].
% 2.88/3.19 367 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(A,D,E,B,F,V6) # label(cls_gb__semiring_Oadd__0_0) # label(axiom). [assumption].
% 2.88/3.19 368 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) | -c_Groebner__Basis_Ogb__semiring(A,E,F,V6,V7,V8) # label(cls_gb__semiring_Oadd__a_0) # label(axiom). [assumption].
% 2.88/3.19 369 hAPP(hAPP(A,B),C) = hAPP(hAPP(A,C),B) | -c_Groebner__Basis_Ogb__semiring(A,D,E,F,V6,V7) # label(cls_gb__semiring_Oadd__c_0) # label(axiom). [assumption].
% 2.88/3.19 370 hAPP(hAPP(A,B),C) = B | -c_Groebner__Basis_Ogb__semiring(D,A,E,B,F,V6) # label(cls_gb__semiring_Omul__0_0) # label(axiom). [assumption].
% 2.88/3.19 371 hAPP(hAPP(A,B),C) = C | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,B,V6) # label(cls_gb__semiring_Omul__1_0) # label(axiom). [assumption].
% 2.88/3.19 372 hAPP(hAPP(A,B),hAPP(hAPP(A,C),D)) = hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) | -c_Groebner__Basis_Ogb__semiring(E,A,F,V6,V7,V8) # label(cls_gb__semiring_Omul__a_0) # label(axiom). [assumption].
% 2.88/3.19 373 hAPP(hAPP(A,B),C) = hAPP(hAPP(A,C),B) | -c_Groebner__Basis_Ogb__semiring(D,A,E,F,V6,V7) # label(cls_gb__semiring_Omul__c_0) # label(axiom). [assumption].
% 2.88/3.19 374 hAPP(hAPP(A,B),hAPP(hAPP(C,D),E)) = hAPP(hAPP(C,hAPP(hAPP(A,B),D)),hAPP(hAPP(A,B),E)) | -c_Groebner__Basis_Ogb__semiring(C,A,F,V6,V7,V8) # label(cls_gb__semiring_Omul__d_0) # label(axiom). [assumption].
% 2.88/3.19 375 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),E) = hAPP(hAPP(B,hAPP(hAPP(A,C),E)),hAPP(hAPP(A,D),E)) | -c_Groebner__Basis_Ogb__semiring(F,B,A,V6,V7,V8) # label(cls_gb__semiring_Opwr__mul_0) # label(axiom). [assumption].
% 2.88/3.19 376 hAPP(hAPP(A,hAPP(hAPP(B,C),D)),hAPP(hAPP(B,C),E)) = hAPP(hAPP(B,C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),E)) | -c_Groebner__Basis_Ogb__semiring(F,A,B,V6,V7,V8) # label(cls_gb__semiring_Omul__pwr_0) # label(axiom). [assumption].
% 2.88/3.19 377 hAPP(hAPP(A,B),c_HOL_Oone__class_Oone(tc_nat)) = B | -c_Groebner__Basis_Ogb__semiring(C,D,A,E,F,V6) # label(cls_gb__semiring_Osemiring__rules_I33_J_0) # label(axiom). [assumption].
% 2.88/3.19 378 hAPP(hAPP(A,B),c_HOL_Ozero__class_Ozero(tc_nat)) = C | -c_Groebner__Basis_Ogb__semiring(D,E,A,F,C,V6) # label(cls_gb__semiring_Opwr__0_0) # label(axiom). [assumption].
% 2.88/3.19 379 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].
% 2.88/3.19 380 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].
% 2.88/3.19 381 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].
% 2.88/3.19 382 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].
% 2.88/3.19 383 hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D) = hAPP(hAPP(A,B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) | -c_Groebner__Basis_Ogb__semiring(E,F,A,V6,V7,V8) # label(cls_gb__semiring_Opwr__pwr_0) # label(axiom). [assumption].
% 2.88/3.19 384 hAPP(hAPP(A,B),B) = hAPP(hAPP(C,B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) | -c_Groebner__Basis_Ogb__semiring(D,A,C,E,F,V6) # label(cls_gb__semiring_Osemiring__rules_I29_J_0) # label(axiom). [assumption].
% 2.88/3.19 385 hAPP(hAPP(A,B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C)) = hAPP(hAPP(D,hAPP(hAPP(A,B),C)),hAPP(hAPP(A,B),C)) | -c_Groebner__Basis_Ogb__semiring(E,D,A,F,V6,V7) # label(cls_gb__semiring_Osemiring__rules_I36_J_0) # label(axiom). [assumption].
% 2.88/3.19 386 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].
% 2.88/3.19 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(341,a,343,b)].
% 2.88/3.19 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(341,a,344,b)].
% 2.88/3.19 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(341,a,345,b)].
% 2.88/3.19 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(341,a,346,b)].
% 2.88/3.19 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(341,a,347,b)].
% 2.88/3.19 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(341,a,361,b)].
% 2.88/3.19 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(341,a,362,b)].
% 2.88/3.19 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(341,a,363,b)].
% 2.88/3.19 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(341,a,364,b)].
% 2.88/3.19 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(341,a,365,b)].
% 2.88/3.19 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(341,a,366,b)].
% 2.88/3.20 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(341,a,376,b)].
% 2.88/3.20 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(341,a,377,b)].
% 2.88/3.20 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(341,a,378,b)].
% 2.88/3.20 387 c_Groebner__Basis_Ogb__semiring(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(289,a,257,a)].
% 2.88/3.20 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(387,a,343,b)].
% 2.88/3.20 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(387,a,344,b)].
% 2.88/3.20 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(387,a,345,b)].
% 2.88/3.20 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A) = A. [resolve(387,a,346,b)].
% 2.88/3.20 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(387,a,347,b)].
% 2.88/3.20 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(387,a,361,b)].
% 2.88/3.20 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(387,a,362,b)].
% 2.88/3.20 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(387,a,363,b)].
% 2.88/3.20 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(387,a,364,b)].
% 2.88/3.20 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(387,a,365,b)].
% 2.88/3.20 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(387,a,366,b)].
% 2.88/3.20 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(387,a,376,b)].
% 2.88/3.20 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(387,a,377,b)].
% 2.88/3.20 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(387,a,378,b)].
% 3.18/3.42 388 class_Divides_Oring__div(tc_Int_Oint) # label(clsarity_Int__Oint__Divides_Oring__div) # label(axiom). [assumption].
% 3.18/3.42 389 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_Divides_Odiv__class_Omod(B,D,A)),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__diff__eq_0) # label(axiom). [assumption].
% 3.18/3.42 390 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),c_Divides_Odiv__class_Omod(B,D,A)),C),D,A) # label(cls_mod__diff__left__eq_0) # label(axiom). [assumption].
% 3.18/3.42 391 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),C),D,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A) # label(cls_mod__diff__right__eq_0) # label(axiom). [assumption].
% 3.18/3.42 392 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(E,C,A) != c_Divides_Odiv__class_Omod(F,C,A) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),E),B),C,A) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),F),D),C,A) # label(cls_mod__diff__cong_0) # label(axiom). [assumption].
% 3.18/3.42 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint)),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)),C,tc_Int_Oint). [resolve(388,a,389,a)].
% 3.18/3.42 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint)),B),C,tc_Int_Oint). [resolve(388,a,390,a)].
% 3.18/3.42 Derived: c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),B),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint)),C,tc_Int_Oint). [resolve(388,a,391,a)].
% 3.18/3.42 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(C,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(D,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(E,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),D),A),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),E),C),B,tc_Int_Oint). [resolve(388,a,392,a)].
% 3.18/3.42 393 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.18/3.42 394 -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].
% 3.18/3.42 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(393,a,394,a)].
% 3.18/3.42 395 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.18/3.42 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(395,a,394,a)].
% 3.18/3.42 396 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 3.18/3.42 397 -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].
% 3.18/3.42 398 -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].
% 3.33/3.59 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(396,a,398,a)].
% 3.33/3.59 399 class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 3.33/3.59 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(399,a,398,a)].
% 3.33/3.59 400 class_OrderedGroup_Olordered__ab__group__add__meet(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__meet) # label(axiom). [assumption].
% 3.33/3.59 401 -class_OrderedGroup_Olordered__ab__group__add__meet(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A)) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) # label(cls_add__inf__distrib__left_0) # label(axiom). [assumption].
% 3.33/3.59 402 -class_OrderedGroup_Olordered__ab__group__add__meet(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),D) = c_Lattices_Olower__semilattice__class_Oinf(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_add__inf__distrib__right_0) # label(axiom). [assumption].
% 3.33/3.59 403 class_Ring__and__Field_Oring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring) # label(axiom). [assumption].
% 3.33/3.59 404 -class_Ring__and__Field_Oring(A) | hAPP(c_Finite__Set_Osetsum(B,C,A),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(C,tc_bool)),D),c_Set_Oinsert(E,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C))) = hAPP(hAPP(c_HOL_Ominus__class_Ominus(A),hAPP(c_Finite__Set_Osetsum(B,C,A),D)),hAPP(B,E)) | -hBOOL(hAPP(hAPP(c_in(C),E),D)) | -c_Finite__Set_Ofinite(D,C) # label(cls_setsum__diff1__ring_0) # label(axiom). [assumption].
% 3.33/3.59 405 -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].
% 3.33/3.59 406 -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].
% 3.33/3.59 407 -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].
% 3.33/3.59 408 -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].
% 3.33/3.59 409 -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].
% 3.42/3.68 410 -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].
% 3.42/3.68 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(403,a,405,a)].
% 3.42/3.68 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(403,a,406,a)].
% 3.42/3.68 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(403,a,407,a)].
% 3.42/3.68 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(403,a,408,a)].
% 3.42/3.68 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(403,a,409,a)].
% 3.42/3.68 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(403,a,410,a)].
% 3.42/3.68 411 class_Ring__and__Field_Opordered__ring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 3.42/3.68 412 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F))) | -hBOOL(hAPP(c_lessequals(D,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),E),B)),C)),F))) # label(cls_le__add__iff2_1) # label(axiom). [assumption].
% 3.42/3.68 413 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(B,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),C),D)),E)),F))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)),B),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)),F))) # label(cls_le__add__iff2_0) # label(axiom). [assumption].
% 3.42/3.68 414 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),F))) | -hBOOL(hAPP(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),A),F)) # label(cls_le__add__iff1_1) # label(axiom). [assumption].
% 3.42/3.68 415 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(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),A),F)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),E),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),F))) # label(cls_le__add__iff1_0) # label(axiom). [assumption].
% 3.42/3.68 416 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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),C)),D)),E)),F)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),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))) # label(cls_less__add__iff1_0) # label(axiom). [assumption].
% 3.42/3.68 417 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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),E)),C)),D)),F)) # label(cls_less__add__iff1_1) # label(axiom). [assumption].
% 3.42/3.68 418 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),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))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),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))) # label(cls_less__add__iff2_0) # label(axiom). [assumption].
% 3.42/3.68 419 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),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_less__add__iff2_1) # label(axiom). [assumption].
% 3.42/3.68 420 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(D,A),C)) # label(cls_mult__left__mono__neg_0) # label(axiom). [assumption].
% 3.42/3.68 421 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(D,A),B)) # label(cls_mult__right__mono__neg_0) # label(axiom). [assumption].
% 3.42/3.68 422 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_split__mult__pos__le_0) # label(axiom). [assumption].
% 3.42/3.68 423 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_split__mult__pos__le_1) # label(axiom). [assumption].
% 3.42/3.68 424 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__nonpos__nonpos_0) # label(axiom). [assumption].
% 3.42/3.68 Derived: hBOOL(hAPP(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),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | -hBOOL(hAPP(c_lessequals(C,tc_Int_Oint),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(411,a,412,a)].
% 3.42/3.68 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),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))) | -hBOOL(hAPP(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),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D)),E))). [resolve(411,a,413,a)].
% 3.42/3.68 Derived: hBOOL(hAPP(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),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | -hBOOL(hAPP(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),tc_Int_Oint),E)). [resolve(411,a,414,a)].
% 3.42/3.68 Derived: hBOOL(hAPP(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),tc_Int_Oint),E)) | -hBOOL(hAPP(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),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)),E))). [resolve(411,a,415,a)].
% 3.42/3.68 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),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)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),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))). [resolve(411,a,416,a)].
% 3.42/3.68 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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)),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),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(411,a,417,a)].
% 3.42/3.68 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),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))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),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))). [resolve(411,a,418,a)].
% 3.57/3.84 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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)),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),D),B)),E))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),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(411,a,419,a)].
% 3.57/3.84 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(C,tc_Int_Oint),B)). [resolve(411,a,420,a)].
% 3.57/3.84 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(C,tc_Int_Oint),A)). [resolve(411,a,421,a)].
% 3.57/3.84 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(411,a,422,a)].
% 3.57/3.84 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(411,a,423,a)].
% 3.57/3.84 425 class_OrderedGroup_Ogroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 3.57/3.84 426 -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].
% 3.57/3.84 427 -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].
% 3.57/3.84 428 -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].
% 3.57/3.84 429 -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].
% 3.57/3.84 430 -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].
% 3.57/3.84 431 -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].
% 3.57/3.84 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(425,a,426,a)].
% 3.57/3.84 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(425,a,427,a)].
% 3.57/3.84 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(425,a,429,a)].
% 3.57/3.84 432 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 3.57/3.84 433 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 3.86/4.16 434 class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 3.86/4.16 435 class_Orderings_Owellorder(tc_nat) # label(clsarity_nat__Orderings_Owellorder) # label(axiom). [assumption].
% 3.86/4.16 436 -class_Orderings_Owellorder(A) | -hBOOL(hAPP(B,C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),c_Orderings_Oord__class_OLeast(B,A))) # label(cls_not__less__Least_0) # label(axiom). [assumption].
% 3.86/4.16 437 -class_Orderings_Owellorder(A) | hBOOL(hAPP(c_lessequals(c_Orderings_Oord__class_OLeast(B,A),A),C)) | -hBOOL(hAPP(B,C)) # label(cls_Least__le_0) # label(axiom). [assumption].
% 3.86/4.16 438 -class_Orderings_Owellorder(A) | hBOOL(hAPP(B,c_Orderings_Oord__class_OLeast(B,A))) | -hBOOL(hAPP(B,C)) # label(cls_LeastI__ex_0) # label(axiom). [assumption].
% 3.86/4.16 439 -class_Orderings_Owellorder(A) | hBOOL(hAPP(B,c_Orderings_Oord__class_OLeast(B,A))) | -hBOOL(hAPP(B,C)) # label(cls_LeastI_0) # label(axiom). [assumption].
% 3.86/4.16 Derived: -hBOOL(hAPP(A,B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),c_Orderings_Oord__class_OLeast(A,tc_nat))). [resolve(435,a,436,a)].
% 3.86/4.16 Derived: hBOOL(hAPP(c_lessequals(c_Orderings_Oord__class_OLeast(A,tc_nat),tc_nat),B)) | -hBOOL(hAPP(A,B)). [resolve(435,a,437,a)].
% 3.86/4.16 Derived: hBOOL(hAPP(A,c_Orderings_Oord__class_OLeast(A,tc_nat))) | -hBOOL(hAPP(A,B)). [resolve(435,a,438,a)].
% 3.86/4.16 440 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.86/4.16 441 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 3.86/4.16 442 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 3.86/4.16 443 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 3.86/4.16 444 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 3.86/4.16 445 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 3.86/4.16 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(440,a,441,a)].
% 3.86/4.16 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)). [resolve(440,a,442,a)].
% 3.86/4.16 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(440,a,443,a)].
% 3.92/4.23 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(440,a,444,a)].
% 3.92/4.23 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(440,a,445,a)].
% 3.92/4.23 446 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 3.92/4.23 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(446,a,441,a)].
% 3.92/4.23 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),B),C)). [resolve(446,a,442,a)].
% 3.92/4.23 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(446,a,443,a)].
% 3.92/4.23 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),B),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(446,a,444,a)].
% 3.92/4.23 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(446,a,445,a)].
% 3.92/4.23 447 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 3.92/4.23 448 -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].
% 3.92/4.23 449 -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].
% 3.92/4.23 450 -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].
% 3.92/4.23 451 -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].
% 3.92/4.23 452 -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].
% 3.92/4.23 453 -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].
% 3.92/4.24 454 -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].
% 3.92/4.24 455 -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].
% 3.92/4.24 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(447,a,448,a)].
% 3.92/4.24 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(447,a,449,a)].
% 3.92/4.24 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(447,a,450,a)].
% 3.92/4.24 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(447,a,451,a)].
% 3.92/4.24 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(447,a,452,a)].
% 3.92/4.24 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(447,a,454,a)].
% 3.92/4.24 456 class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 3.92/4.24 Derived: c_HOL_Ozero__class_Ozero(tc_Int_Oint) != c_HOL_Oone__class_Oone(tc_Int_Oint). [resolve(456,a,448,a)].
% 3.92/4.24 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(456,a,449,a)].
% 3.92/4.24 Derived: c_HOL_Oone__class_Oone(tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(456,a,450,a)].
% 3.92/4.24 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(456,a,451,a)].
% 3.92/4.24 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(456,a,452,a)].
% 3.92/4.24 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(456,a,454,a)].
% 4.16/4.47 457 class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) # label(axiom). [assumption].
% 4.16/4.47 458 -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].
% 4.16/4.47 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(457,a,458,a)].
% 4.16/4.47 459 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 4.16/4.47 460 -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].
% 4.16/4.47 461 -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].
% 4.16/4.47 462 class_OrderedGroup_Omonoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 4.16/4.47 463 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 4.16/4.47 464 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_mult__less__le__imp__less_0) # label(axiom). [assumption].
% 4.16/4.47 465 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__le__less__imp__less_0) # label(axiom). [assumption].
% 4.16/4.47 466 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_mult__strict__mono_H_0) # label(axiom). [assumption].
% 4.16/4.47 467 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))) # label(cls_mult__less__imp__less__right_0) # label(axiom). [assumption].
% 4.16/4.47 468 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) # label(cls_mult__less__imp__less__left_0) # label(axiom). [assumption].
% 4.16/4.47 469 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_mult__strict__mono_0) # label(axiom). [assumption].
% 4.16/4.47 470 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))) # label(cls_mult__right__le__imp__le_0) # label(axiom). [assumption].
% 4.16/4.47 471 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) # label(cls_mult__left__le__imp__le_0) # label(axiom). [assumption].
% 4.16/4.47 472 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) # label(cls_mult__strict__left__mono_0) # label(axiom). [assumption].
% 4.16/4.47 473 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_mult__strict__right__mono_0) # label(axiom). [assumption].
% 4.16/4.47 474 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_mult__pos__pos_0) # label(axiom). [assumption].
% 4.16/4.47 475 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B))) # label(cls_zero__less__mult__pos_0) # label(axiom). [assumption].
% 4.16/4.47 476 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) # label(cls_zero__less__mult__pos2_0) # label(axiom). [assumption].
% 4.16/4.47 477 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__neg__pos_0) # label(axiom). [assumption].
% 4.16/4.47 478 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_mult__pos__neg_0) # label(axiom). [assumption].
% 4.16/4.47 479 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),C)) # label(cls_mult__pos__neg2_0) # label(axiom). [assumption].
% 4.16/4.47 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(463,a,464,a)].
% 4.16/4.47 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(463,a,465,a)].
% 4.16/4.47 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(463,a,466,a)].
% 4.16/4.47 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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(463,a,467,a)].
% 4.16/4.47 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))). [resolve(463,a,468,a)].
% 4.16/4.47 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(463,a,469,a)].
% 4.16/4.47 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C))). [resolve(463,a,470,a)].
% 4.16/4.47 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))). [resolve(463,a,471,a)].
% 4.16/4.47 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)). [resolve(463,a,472,a)].
% 4.16/4.47 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(463,a,473,a)].
% 4.16/4.47 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(463,a,474,a)].
% 4.16/4.47 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A))). [resolve(463,a,475,a)].
% 4.16/4.47 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))). [resolve(463,a,476,a)].
% 4.16/4.47 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(463,a,477,a)].
% 4.16/4.47 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(463,a,478,a)].
% 4.16/4.47 480 class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 4.16/4.47 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(480,a,464,a)].
% 4.16/4.47 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),B),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(480,a,465,a)].
% 4.16/4.47 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(480,a,466,a)].
% 4.16/4.47 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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(480,a,467,a)].
% 4.16/4.47 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))). [resolve(480,a,468,a)].
% 4.16/4.47 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),B),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(480,a,469,a)].
% 4.23/4.55 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C))). [resolve(480,a,470,a)].
% 4.23/4.55 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),C)) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),A),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))). [resolve(480,a,471,a)].
% 4.23/4.55 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),B),C)). [resolve(480,a,472,a)].
% 4.23/4.55 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(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))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(480,a,473,a)].
% 4.23/4.55 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(480,a,474,a)].
% 4.23/4.55 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A))). [resolve(480,a,475,a)].
% 4.23/4.55 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))). [resolve(480,a,476,a)].
% 4.23/4.55 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(480,a,477,a)].
% 4.23/4.55 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),B),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A)). [resolve(480,a,478,a)].
% 4.23/4.55 481 class_Ring__and__Field_Oordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 4.23/4.55 482 -class_Ring__and__Field_Oordered__semiring(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))) # label(cls_mult__right__less__imp__less_0) # label(axiom). [assumption].
% 4.62/4.86 483 -class_Ring__and__Field_Oordered__semiring(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) # label(cls_mult__left__less__imp__less_0) # label(axiom). [assumption].
% 4.62/4.86 484 class_Ring__and__Field_Oordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 4.62/4.86 485 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 4.62/4.86 486 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) # label(cls_mult__strict__left__mono__comm_0) # label(axiom). [assumption].
% 4.62/4.86 487 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 4.62/4.86 488 class_Ring__and__Field_Omult__mono1(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 4.62/4.86 489 -class_Ring__and__Field_Omult__mono1(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_mult__mono1_0) # label(axiom). [assumption].
% 4.62/4.86 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(488,a,489,a)].
% 4.62/4.86 490 class_Ring__and__Field_Omult__mono1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 4.62/4.86 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),C)). [resolve(490,a,489,a)].
% 4.62/4.86 491 class_Ring__and__Field_Omult__mono(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 4.62/4.86 492 -class_Ring__and__Field_Omult__mono(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),D)) # label(cls_mult__left__mono_0) # label(axiom). [assumption].
% 4.62/4.86 493 -class_Ring__and__Field_Omult__mono(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__right__mono_0) # label(axiom). [assumption].
% 4.62/4.86 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(491,a,493,a)].
% 4.62/4.86 494 class_Ring__and__Field_Omult__mono(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 4.62/4.86 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(494,a,493,a)].
% 4.62/4.86 495 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 4.78/5.09 496 -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].
% 4.78/5.09 497 class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 4.78/5.09 498 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 4.78/5.09 499 -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].
% 4.78/5.09 500 -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].
% 4.78/5.09 501 class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 4.78/5.09 502 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 4.78/5.09 503 -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].
% 4.78/5.09 504 -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].
% 4.78/5.09 505 -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].
% 4.78/5.09 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(502,a,503,a)].
% 4.78/5.09 506 class_Ring__and__Field_Osemiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 4.78/5.09 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(506,a,503,a)].
% 4.78/5.09 507 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 4.78/5.09 508 -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].
% 4.78/5.09 509 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(c_Finite__Set_Osetsum(C,D,A),E)) = hAPP(c_Finite__Set_Osetsum(hAPP(hAPP(c_COMBB(A,A,D),hAPP(c_HOL_Otimes__class_Otimes(A),B)),C),D,A),E) # label(cls_setsum__right__distrib_0) # label(axiom). [assumption].
% 4.78/5.09 510 -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].
% 4.78/5.09 511 -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].
% 4.78/5.09 512 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(c_Finite__Set_Osetsum(B,C,A),D)),E) = hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),C),c_HOL_Otimes__class_Otimes(A)),B),C,A,A),E),C,A),D) # label(cls_setsum__left__distrib_0) # label(axiom). [assumption].
% 4.78/5.09 513 -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].
% 4.78/5.09 514 -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].
% 4.78/5.09 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(c_Finite__Set_Osetsum(B,C,tc_nat),D)) = hAPP(c_Finite__Set_Osetsum(hAPP(hAPP(c_COMBB(tc_nat,tc_nat,C),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A)),B),C,tc_nat),D). [resolve(507,a,509,a)].
% 4.78/5.09 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(507,a,510,a)].
% 4.78/5.09 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(507,a,511,a)].
% 4.78/5.09 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Finite__Set_Osetsum(A,B,tc_nat),C)),D) = hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),B),c_HOL_Otimes__class_Otimes(tc_nat)),A),B,tc_nat,tc_nat),D),B,tc_nat),C). [resolve(507,a,512,a)].
% 4.78/5.09 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(507,a,514,a)].
% 4.78/5.09 515 class_Ring__and__Field_Osemiring__0(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 4.78/5.09 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(c_Finite__Set_Osetsum(B,C,tc_Int_Oint),D)) = hAPP(c_Finite__Set_Osetsum(hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,C),hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A)),B),C,tc_Int_Oint),D). [resolve(515,a,509,a)].
% 4.78/5.09 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(515,a,510,a)].
% 4.78/5.09 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(515,a,511,a)].
% 4.86/5.17 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Finite__Set_Osetsum(A,B,tc_Int_Oint),C)),D) = hAPP(c_Finite__Set_Osetsum(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),B),c_HOL_Otimes__class_Otimes(tc_Int_Oint)),A),B,tc_Int_Oint,tc_Int_Oint),D),B,tc_Int_Oint),C). [resolve(515,a,512,a)].
% 4.86/5.17 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(515,a,514,a)].
% 4.86/5.17 516 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 4.86/5.17 517 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__nonneg__nonneg_0) # label(axiom). [assumption].
% 4.86/5.17 518 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_split__mult__neg__le_0) # label(axiom). [assumption].
% 4.86/5.17 519 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_split__mult__neg__le_1) # label(axiom). [assumption].
% 4.86/5.17 520 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__nonneg__nonpos_0) # label(axiom). [assumption].
% 4.86/5.17 521 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__nonpos__nonneg_0) # label(axiom). [assumption].
% 4.86/5.17 522 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__nonneg__nonpos2_0) # label(axiom). [assumption].
% 4.86/5.17 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(516,a,517,a)].
% 4.86/5.17 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(516,a,518,a)].
% 4.86/5.17 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(516,a,519,a)].
% 4.86/5.17 523 class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 4.86/5.17 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(523,a,518,a)].
% 5.06/5.32 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(523,a,519,a)].
% 5.06/5.32 524 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 5.06/5.32 525 -class_Ring__and__Field_Opordered__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__mono_0) # label(axiom). [assumption].
% 5.06/5.32 526 -class_Ring__and__Field_Opordered__semiring(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__mono_H_0) # label(axiom). [assumption].
% 5.06/5.32 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(524,a,525,a)].
% 5.06/5.32 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(524,a,526,a)].
% 5.06/5.32 527 class_Ring__and__Field_Opordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 5.06/5.32 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(527,a,525,a)].
% 5.06/5.32 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(527,a,526,a)].
% 5.06/5.32 528 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 5.06/5.32 529 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = B | -hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 5.06/5.32 530 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) != C | hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_le__iff__sup_1) # label(axiom). [assumption].
% 5.06/5.32 531 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = C | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 5.06/5.32 532 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A),D)) | -hBOOL(hAPP(c_lessequals(C,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_le__sup__iff_2) # label(axiom). [assumption].
% 5.06/5.32 533 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A),D)) | -hBOOL(hAPP(c_lessequals(C,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_sup__least_0) # label(axiom). [assumption].
% 5.06/5.32 534 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Oupper__semilattice__class_Osup(C,B,A))) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 5.06/5.32 535 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Oupper__semilattice__class_Osup(B,C,A))) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 5.06/5.32 536 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A),D)) | -hBOOL(hAPP(c_lessequals(C,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_le__supI_0) # label(axiom). [assumption].
% 5.06/5.32 537 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_Lattices_Oupper__semilattice__class_Osup(C,D,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_less__supI2_0) # label(axiom). [assumption].
% 5.06/5.32 538 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),c_Lattices_Oupper__semilattice__class_Osup(C,D,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_less__supI1_0) # label(axiom). [assumption].
% 5.06/5.32 539 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),A),C)) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 5.06/5.32 540 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A),C)) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 5.06/5.32 541 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Oupper__semilattice__class_Osup(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 5.06/5.32 542 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),c_Lattices_Oupper__semilattice__class_Osup(C,D,A))) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 5.06/5.32 543 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),A),C)) # label(cls_le__supE_1) # label(axiom). [assumption].
% 5.06/5.32 544 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A),C)) # label(cls_le__supE_0) # label(axiom). [assumption].
% 5.06/5.32 545 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 5.06/5.32 546 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A) # label(cls_sup__left__commute_0) # label(axiom). [assumption].
% 5.06/5.32 547 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) # label(cls_sup__assoc_0) # label(axiom). [assumption].
% 5.06/5.32 548 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = c_Lattices_Oupper__semilattice__class_Osup(C,B,A) # label(cls_sup__commute_0) # label(axiom). [assumption].
% 5.06/5.32 549 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) = c_Lattices_Oupper__semilattice__class_Osup(B,C,A) # label(cls_sup__left__idem_0) # label(axiom). [assumption].
% 5.06/5.32 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = B | -hBOOL(hAPP(c_lessequals(C,tc_fun(D,A)),B)). [resolve(528,a,529,a)].
% 5.06/5.32 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) != C | hBOOL(hAPP(c_lessequals(B,tc_fun(D,A)),C)). [resolve(528,a,530,a)].
% 5.06/5.32 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = C | -hBOOL(hAPP(c_lessequals(B,tc_fun(D,A)),C)). [resolve(528,a,531,a)].
% 5.06/5.32 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),tc_fun(D,A)),E)) | -hBOOL(hAPP(c_lessequals(C,tc_fun(D,A)),E)) | -hBOOL(hAPP(c_lessequals(B,tc_fun(D,A)),E)). [resolve(528,a,532,a)].
% 5.06/5.32 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),c_Lattices_Oupper__semilattice__class_Osup(D,B,tc_fun(C,A)))). [resolve(528,a,534,a)].
% 5.06/5.32 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),c_Lattices_Oupper__semilattice__class_Osup(B,D,tc_fun(C,A)))). [resolve(528,a,535,a)].
% 5.06/5.32 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),C),c_Lattices_Oupper__semilattice__class_Osup(D,E,tc_fun(B,A)))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),C),E)). [resolve(528,a,537,a)].
% 5.06/5.32 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),C),c_Lattices_Oupper__semilattice__class_Osup(D,E,tc_fun(B,A)))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),C),D)). [resolve(528,a,538,a)].
% 5.06/5.32 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),D)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(E,B,tc_fun(C,A)),tc_fun(C,A)),D)). [resolve(528,a,539,a)].
% 5.06/5.32 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),D)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,E,tc_fun(C,A)),tc_fun(C,A)),D)). [resolve(528,a,540,a)].
% 5.06/5.32 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),c_Lattices_Oupper__semilattice__class_Osup(D,E,tc_fun(C,A)))) | -hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),E)). [resolve(528,a,541,a)].
% 5.06/5.32 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),c_Lattices_Oupper__semilattice__class_Osup(D,E,tc_fun(C,A)))) | -hBOOL(hAPP(c_lessequals(B,tc_fun(C,A)),D)). [resolve(528,a,542,a)].
% 5.06/5.32 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(528,a,545,a)].
% 5.06/5.32 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,tc_fun(E,A)),tc_fun(E,A)). [resolve(528,a,546,a)].
% 5.06/5.32 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(528,a,547,a)].
% 5.06/5.32 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(C,B,tc_fun(D,A)). [resolve(528,a,548,a)].
% 5.06/5.32 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)). [resolve(528,a,549,a)].
% 5.06/5.32 550 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 5.06/5.32 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = A | -hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(550,a,529,a)].
% 5.06/5.32 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) != B | hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(550,a,530,a)].
% 5.06/5.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = B | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(550,a,531,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(550,a,532,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat))). [resolve(550,a,534,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat))). [resolve(550,a,535,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(550,a,537,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)). [resolve(550,a,538,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_nat),tc_nat),B)). [resolve(550,a,539,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),tc_nat),B)). [resolve(550,a,540,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(550,a,541,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat))) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(550,a,542,a)].
% 5.06/5.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_nat) = A. [resolve(550,a,545,a)].
% 5.06/5.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),tc_nat). [resolve(550,a,546,a)].
% 5.06/5.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),C,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat). [resolve(550,a,547,a)].
% 5.06/5.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat). [resolve(550,a,548,a)].
% 5.06/5.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat). [resolve(550,a,549,a)].
% 5.06/5.33 551 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 5.06/5.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -hBOOL(hAPP(c_lessequals(B,tc_bool),A)). [resolve(551,a,529,a)].
% 5.06/5.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | hBOOL(hAPP(c_lessequals(A,tc_bool),B)). [resolve(551,a,530,a)].
% 5.06/5.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -hBOOL(hAPP(c_lessequals(A,tc_bool),B)). [resolve(551,a,531,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool),C)) | -hBOOL(hAPP(c_lessequals(B,tc_bool),C)) | -hBOOL(hAPP(c_lessequals(A,tc_bool),C)). [resolve(551,a,532,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool))). [resolve(551,a,534,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool))). [resolve(551,a,535,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),C)). [resolve(551,a,537,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),B)). [resolve(551,a,538,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),B)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_bool),tc_bool),B)). [resolve(551,a,539,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),B)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),tc_bool),B)). [resolve(551,a,540,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool))) | -hBOOL(hAPP(c_lessequals(A,tc_bool),C)). [resolve(551,a,541,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool))) | -hBOOL(hAPP(c_lessequals(A,tc_bool),B)). [resolve(551,a,542,a)].
% 5.06/5.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(551,a,545,a)].
% 5.06/5.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),tc_bool). [resolve(551,a,546,a)].
% 5.06/5.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),C,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool). [resolve(551,a,547,a)].
% 5.06/5.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool). [resolve(551,a,548,a)].
% 5.06/5.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool). [resolve(551,a,549,a)].
% 5.06/5.33 552 class_Lattices_Oupper__semilattice(tc_Int_Oint) # label(clsarity_Int__Oint__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 5.06/5.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint) = A | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(552,a,529,a)].
% 5.06/5.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint) != B | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(552,a,530,a)].
% 5.06/5.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint) = B | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(552,a,531,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(552,a,532,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_Int_Oint))). [resolve(552,a,534,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint))). [resolve(552,a,535,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),C)). [resolve(552,a,537,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_Int_Oint))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_Int_Oint),A),B)). [resolve(552,a,538,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_Int_Oint),tc_Int_Oint),B)). [resolve(552,a,539,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_Int_Oint),tc_Int_Oint),B)). [resolve(552,a,540,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(552,a,541,a)].
% 5.06/5.33 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(552,a,542,a)].
% 5.06/5.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_Int_Oint) = A. [resolve(552,a,545,a)].
% 5.06/5.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_Int_Oint),tc_Int_Oint) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(552,a,546,a)].
% 5.46/5.72 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(552,a,547,a)].
% 5.46/5.72 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_Int_Oint). [resolve(552,a,548,a)].
% 5.46/5.72 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint),tc_Int_Oint) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint). [resolve(552,a,549,a)].
% 5.46/5.72 553 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 5.46/5.72 554 -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].
% 5.46/5.72 555 -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].
% 5.46/5.72 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(553,a,555,a)].
% 5.46/5.72 556 class_Ring__and__Field_Osemiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 5.46/5.72 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(556,a,555,a)].
% 5.46/5.72 557 class_OrderedGroup_Olordered__ab__group__add__join(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__join) # label(axiom). [assumption].
% 5.46/5.72 558 -class_OrderedGroup_Olordered__ab__group__add__join(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Lattices_Oupper__semilattice__class_Osup(B,C,A)),D) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A) # label(cls_add__sup__distrib__right_0) # label(axiom). [assumption].
% 5.46/5.72 559 -class_OrderedGroup_Olordered__ab__group__add__join(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Lattices_Oupper__semilattice__class_Osup(C,D,A)) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A) # label(cls_add__sup__distrib__left_0) # label(axiom). [assumption].
% 5.46/5.72 560 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].
% 5.46/5.72 561 -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].
% 5.46/5.72 562 -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].
% 5.46/5.72 563 -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].
% 5.46/5.72 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(560,a,563,a)].
% 8.20/8.50 564 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 8.20/8.50 565 -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].
% 8.20/8.50 566 class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 8.20/8.50
% 8.20/8.50 ============================== end predicate elimination =============
% 8.20/8.50
% 8.20/8.50 Auto_denials: (non-Horn, no changes).
% 8.20/8.50
% 8.20/8.50 Term ordering decisions:
% 8.20/8.50 Function symbol KB weights: tc_nat=1. tc_Int_Oint=1. tc_bool=1. c_Suc=1. c_Int_OPls=1. t_a=1. c_Int_OMin=1. c_and=1. v_x=1. t_b=1. c_or=1. v_f=1. c_Not=1. v_A=1. v_n=1. hAPP=1. c_lessequals=1. tc_fun=1. c_Int_Onumber__class_Onumber__of=1. c_SetInterval_Oord__class_OatLeastLessThan=1. c_SEQ_OLIMSEQ=1. c_Series_Osums=1. c_Series_Osummable=1. c_List_Oset=1. c_Orderings_Oord__class_OLeast=1. c_List_Osko__List__Xall__nat__less__eq__1__1=1. c_List_Osko__List__Xex__nat__less__eq__1__2=1. tc_prod=1. c_HOL_Ozero__class_Ozero=1. c_HOL_Oplus__class_Oplus=1. c_HOL_Oord__class_Oless=1. c_HOL_Otimes__class_Otimes=1. c_Power_Opower__class_Opower=1. c_HOL_Ominus__class_Ominus=1. c_Int_OBit1=1. c_Int_OBit0=1. c_HOL_Oone__class_Oone=1. c_in=1. c_Orderings_Obot__class_Obot=1. c_Collect=1. c_fequal=1. c_Ex=1. c_Parity_Osko__Parity__Xodd__Suc__mult__two__ex__1__1=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Divides_Odiv__class_Omod=1. c_COMBB=1. c_Divides_Odiv__class_Odiv=1. c_Finite__Set_Osetsum=1. c_Power_Opower_Opower=1. c_Set_Oinsert=1. c_List_Ofilter=1. c_COMBS=1. c_COMBC=1. c_Set_Oimage=1. c_Relation_OImage=1. c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bex__1__1=1. c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bounded__ex__1__1=1. c_split=1.
% 8.20/8.50
% 8.20/8.50 ============================== end of process initial clauses ========
% 8.20/8.50
% 8.20/8.50 ============================== CLAUSES FOR SEARCH ====================
% 8.20/8.50
% 8.20/8.50 ============================== end of clauses for search =============
% 8.20/8.50
% 8.20/8.50 ============================== SEARCH ================================
% 8.20/8.50
% 8.20/8.50 % Starting search at 4.46 seconds.
% 8.20/8.50
% 8.20/8.50 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 140 (0.00 of 4.77 sec).
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=72.000, iters=3591
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=67.000, iters=3537
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=65.000, iters=3515
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=61.000, iters=3395
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=60.000, iters=3500
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=55.000, iters=3438
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=53.000, iters=3365
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=51.000, iters=3510
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=47.000, iters=3335
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=46.000, iters=3337
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=45.000, iters=3370
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=44.000, iters=3339
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=43.000, iters=3338
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=42.000, iters=3383
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=41.000, iters=3351
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=40.000, iters=3399
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=38.000, iters=3364
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=37.000, iters=3419
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=35.000, iters=3514
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=34.000, iters=3480
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=33.000, iters=3389
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=32.000, iters=3356
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=31.000, iters=3335
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=30.000, iters=3352
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=29.000, iters=3336
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=28.000, iters=3341
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=27.000, iters=3348
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=26.000, iters=3351
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=25.000, iters=3337
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=24.000, iters=3333
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=23.000, iters=3387
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=22.000, iters=3345
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=21.000, iters=3337
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=20.000, iters=3628
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=19.000, iters=3388
% 8.20/8.50
% 8.20/8.50 Low Water (displace): id=14274, wt=15.000
% 8.20/8.50
% 8.20/8.50 Low Water (displace): id=14324, wt=14.000
% 8.20/8.50
% 8.20/8.50 Low Water (keep): wt=18.000, iters=3350
% 8.20/8.50
% 8.20/8.50 Low Water (displace): id=16404, wt=13.000
% 21.75/22.00
% 21.75/22.00 Low Water (displace): id=17959, wt=12.000
% 21.75/22.00
% 21.75/22.00 Low Water (keep): wt=17.000, iters=3378
% 21.75/22.00
% 21.75/22.00 Low Water (keep): wt=16.000, iters=3333
% 21.75/22.00
% 21.75/22.00 ============================== PROOF =================================
% 21.75/22.00 % SZS status Unsatisfiable
% 21.75/22.00 % SZS output start Refutation
% 21.75/22.00
% 21.75/22.00 % Proof 1 at 19.99 (+ 0.36) seconds.
% 21.75/22.00 % Length of proof is 32.
% 21.75/22.00 % Level of proof is 7.
% 21.75/22.00 % Maximum clause weight is 38.000.
% 21.75/22.00 % Given clauses 7595.
% 21.75/22.00
% 21.75/22.00 1 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 21.75/22.00 6 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,C,A),c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool))) = c_HOL_Ozero__class_Ozero(A) # label(cls_setsum__empty_0) # label(axiom). [assumption].
% 21.75/22.00 21 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(c_Finite__Set_Osetsum(B,C,A),c_Set_Oinsert(D,E,C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,D)),hAPP(c_Finite__Set_Osetsum(B,C,A),E)) | hBOOL(hAPP(hAPP(c_in(C),D),E)) | -c_Finite__Set_Ofinite(E,C) # label(cls_setsum__insert_0) # label(axiom). [assumption].
% 21.75/22.00 733 c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A) # label(cls_finite_OemptyI_0) # label(axiom). [assumption].
% 21.75/22.00 815 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A) # label(cls_nat__add__commute_0) # label(axiom). [assumption].
% 21.75/22.00 1041 -hBOOL(hAPP(hAPP(c_in(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)))) # label(cls_emptyE_0) # label(axiom). [assumption].
% 21.75/22.00 1066 hAPP(c_Collect(A),hAPP(c_fequal(A),B)) = c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A) # label(cls_singleton__conv2_0) # label(axiom). [assumption].
% 21.75/22.00 1067 c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B) = hAPP(c_Collect(B),hAPP(c_fequal(B),A)). [copy(1066),flip(a)].
% 21.75/22.00 1149 A != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_natgb_Oadd__r0__iff_0) # label(axiom). [assumption].
% 21.75/22.00 1150 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != A | c_HOL_Ozero__class_Ozero(tc_nat) = B. [copy(1149),flip(a),flip(b)].
% 21.75/22.00 1155 A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) # label(cls_natgb_Oadd__r0__iff_1) # label(axiom). [assumption].
% 21.75/22.00 1156 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [copy(1155),flip(a)].
% 21.75/22.00 1245 hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(c_Suc,B)) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)) # label(cls_add__Suc__right_0) # label(axiom). [assumption].
% 21.75/22.00 1428 hAPP(c_Collect(A),hAPP(c_COMBC(c_fequal(A),A,A,tc_bool),B)) = c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A) # label(cls_singleton__conv_0) # label(axiom). [assumption].
% 21.75/22.00 1429 hAPP(c_Collect(A),hAPP(c_COMBC(c_fequal(A),A,A,tc_bool),B)) = hAPP(c_Collect(A),hAPP(c_fequal(A),B)). [copy(1428),rewrite([1067(10)])].
% 21.75/22.00 1489 c_Lattices_Oupper__semilattice__class_Osup(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),tc_fun(B,tc_bool)) = A # label(cls_Un__empty__right_0) # label(axiom). [assumption].
% 21.75/22.00 1549 c_Set_Oinsert(A,B,C) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Collect(C),hAPP(c_COMBC(c_fequal(C),C,C,tc_bool),A)),B,tc_fun(C,tc_bool)) # label(cls_insert__def_0) # label(axiom). [assumption].
% 21.75/22.00 1550 c_Set_Oinsert(A,B,C) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_Collect(C),hAPP(c_fequal(C),A)),B,tc_fun(C,tc_bool)). [copy(1549),rewrite([1429(7)])].
% 21.75/22.00 1627 hAPP(c_Suc,A) != c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_nat_Osimps_I3_J_0) # label(axiom). [assumption].
% 21.75/22.00 1643 hAPP(c_Collect(A),B) = B # label(cls_Collect__def_0) # label(axiom). [assumption].
% 21.75/22.00 1679 hAPP(hAPP(hAPP(c_COMBB(A,B,C),D),E),F) = hAPP(D,hAPP(E,F)) # label(cls_COMBB__def_0) # label(axiom). [assumption].
% 21.75/22.00 1681 hAPP(hAPP(c_COMBS(A,B,C,D),E),F) = hAPP(hAPP(A,F),hAPP(E,F)) # label(cls_COMBS__def_0) # label(axiom). [assumption].
% 21.75/22.00 1753 hAPP(c_Finite__Set_Osetsum(A,B,tc_nat),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,6,a)].
% 21.75/22.01 1769 hAPP(c_Finite__Set_Osetsum(A,B,tc_nat),c_Set_Oinsert(C,D,B)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,C)),hAPP(c_Finite__Set_Osetsum(A,B,tc_nat),D)) | hBOOL(hAPP(hAPP(c_in(B),C),D)) | -c_Finite__Set_Ofinite(D,B). [resolve(1,a,21,a)].
% 21.75/22.01 1770 hAPP(c_Finite__Set_Osetsum(A,B,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(B),C),D,tc_fun(B,tc_bool))) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,C)),hAPP(c_Finite__Set_Osetsum(A,B,tc_nat),D)) | hBOOL(hAPP(hAPP(c_in(B),C),D)) | -c_Finite__Set_Ofinite(D,B). [copy(1769),rewrite([1550(3),1643(6)])].
% 21.75/22.01 4948 hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)) != A. [para(1245(a,1),1150(a,1)),flip(b),unit_del(b,1627)].
% 21.75/22.01 6941 hAPP(hAPP(c_COMBS(hAPP(c_COMBB(A,B,C),D),E,F,V6),V7),V8) = hAPP(D,hAPP(V8,hAPP(V7,V8))). [para(1681(a,2),1679(a,1))].
% 21.75/22.01 7237 hAPP(c_Finite__Set_Osetsum(A,B,tc_nat),hAPP(c_fequal(B),C)) = hAPP(A,C). [resolve(1770,c,733,a),rewrite([1489(10),1753(15),1156(12)]),unit_del(b,1041)].
% 21.75/22.01 10831 hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)) != B. [para(815(a,1),4948(a,1,2))].
% 21.75/22.01 10987 hAPP(c_Suc,hAPP(hAPP(c_COMBS(c_HOL_Oplus__class_Oplus(tc_nat),A,B,C),D),E)) != hAPP(D,E). [para(1681(a,2),10831(a,1,2))].
% 21.75/22.01 65293 hAPP(c_Suc,hAPP(hAPP(c_COMBS(c_HOL_Oplus__class_Oplus(tc_nat),A,B,C),c_Finite__Set_Osetsum(D,E,tc_nat)),hAPP(c_fequal(E),F))) != hAPP(D,F). [para(7237(a,1),10987(a,2))].
% 21.75/22.01 65294 $F. [resolve(65293,a,6941,a(flip))].
% 21.75/22.01
% 21.75/22.01 % SZS output end Refutation
% 21.75/22.01 ============================== end of proof ==========================
% 21.75/22.01
% 21.75/22.01 ============================== STATISTICS ============================
% 21.75/22.01
% 21.75/22.01 Given=7595. Generated=593275. Kept=64145. proofs=1.
% 21.75/22.01 Usable=7460. Sos=9997. Demods=2058. Limbo=1, Disabled=49080. Hints=0.
% 21.75/22.01 Megabytes=62.43.
% 21.75/22.01 User_CPU=19.99, System_CPU=0.36, Wall_clock=20.
% 21.75/22.01
% 21.75/22.01 ============================== end of statistics =====================
% 21.75/22.01
% 21.75/22.01 ============================== end of search =========================
% 21.75/22.01
% 21.75/22.01 THEOREM PROVED
% 21.75/22.01 % SZS status Unsatisfiable
% 21.75/22.01
% 21.75/22.01 Exiting with 1 proof.
% 21.75/22.01
% 21.75/22.01 Process 7592 exit (max_proofs) Tue Jun 14 20:04:12 2022
% 21.75/22.01 Prover9 interrupted
%------------------------------------------------------------------------------