TSTP Solution File: SWV586-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV586-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.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 21:13:59 EDT 2022
% Result : Timeout 300.03s 300.26s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SWV586-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.10/0.31 % Computer : n014.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 600
% 0.10/0.31 % DateTime : Tue Jun 14 21:09:51 EDT 2022
% 0.16/0.31 % CPUTime :
% 1.94/2.20 ============================== Prover9 ===============================
% 1.94/2.20 Prover9 (32) version 2009-11A, November 2009.
% 1.94/2.20 Process 27940 was started by sandbox2 on n014.cluster.edu,
% 1.94/2.20 Tue Jun 14 21:09:53 2022
% 1.94/2.20 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_27778_n014.cluster.edu".
% 1.94/2.20 ============================== end of head ===========================
% 1.94/2.20
% 1.94/2.20 ============================== INPUT =================================
% 1.94/2.20
% 1.94/2.20 % Reading from file /tmp/Prover9_27778_n014.cluster.edu
% 1.94/2.20
% 1.94/2.20 set(prolog_style_variables).
% 1.94/2.20 set(auto2).
% 1.94/2.20 % set(auto2) -> set(auto).
% 1.94/2.20 % set(auto) -> set(auto_inference).
% 1.94/2.20 % set(auto) -> set(auto_setup).
% 1.94/2.20 % set(auto_setup) -> set(predicate_elim).
% 1.94/2.20 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.94/2.20 % set(auto) -> set(auto_limits).
% 1.94/2.20 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.94/2.20 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.94/2.20 % set(auto) -> set(auto_denials).
% 1.94/2.20 % set(auto) -> set(auto_process).
% 1.94/2.20 % set(auto2) -> assign(new_constants, 1).
% 1.94/2.20 % set(auto2) -> assign(fold_denial_max, 3).
% 1.94/2.20 % set(auto2) -> assign(max_weight, "200.000").
% 1.94/2.20 % set(auto2) -> assign(max_hours, 1).
% 1.94/2.20 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.94/2.20 % set(auto2) -> assign(max_seconds, 0).
% 1.94/2.20 % set(auto2) -> assign(max_minutes, 5).
% 1.94/2.20 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.94/2.20 % set(auto2) -> set(sort_initial_sos).
% 1.94/2.20 % set(auto2) -> assign(sos_limit, -1).
% 1.94/2.20 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.94/2.20 % set(auto2) -> assign(max_megs, 400).
% 1.94/2.20 % set(auto2) -> assign(stats, some).
% 1.94/2.20 % set(auto2) -> clear(echo_input).
% 1.94/2.20 % set(auto2) -> set(quiet).
% 1.94/2.20 % set(auto2) -> clear(print_initial_clauses).
% 1.94/2.20 % set(auto2) -> clear(print_given).
% 1.94/2.20 assign(lrs_ticks,-1).
% 1.94/2.20 assign(sos_limit,10000).
% 1.94/2.20 assign(order,kbo).
% 1.94/2.20 set(lex_order_vars).
% 1.94/2.20 clear(print_given).
% 1.94/2.20
% 1.94/2.20 % formulas(sos). % not echoed (1855 formulas)
% 1.94/2.20
% 1.94/2.20 ============================== end of input ==========================
% 1.94/2.20
% 1.94/2.20 % From the command line: assign(max_seconds, 300).
% 1.94/2.20
% 1.94/2.20 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.94/2.20
% 1.94/2.20 % Formulas that are not ordinary clauses:
% 1.94/2.20
% 1.94/2.20 ============================== end of process non-clausal formulas ===
% 1.94/2.20
% 1.94/2.20 ============================== PROCESS INITIAL CLAUSES ===============
% 1.94/2.20
% 1.94/2.20 ============================== PREDICATE ELIMINATION =================
% 1.94/2.20 1 class_Power_Opower(tc_nat) # label(clsarity_nat__Power_Opower) # label(axiom). [assumption].
% 1.94/2.20 2 -class_Power_Opower(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_power__0_0) # label(axiom). [assumption].
% 1.94/2.20 3 -class_Power_Opower(A) | c_Power_Opower__class_Opower(A) = c_Power_Opower_Opower(c_HOL_Oone__class_Oone(A),c_HOL_Otimes__class_Otimes(A),A) # label(cls_power__power__power_0) # label(axiom). [assumption].
% 1.94/2.20 4 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_0) # label(axiom). [assumption].
% 1.94/2.20 5 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(A) # label(cls_power__0__left_0) # label(axiom). [assumption].
% 1.94/2.20 6 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_1) # label(axiom). [assumption].
% 1.94/2.20 7 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__eq__0__iff_2) # label(axiom). [assumption].
% 1.94/2.20 8 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__0__left_1) # label(axiom). [assumption].
% 1.94/2.20 9 -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].
% 1.94/2.20 10 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff__number__of_0) # label(axiom). [assumption].
% 1.94/2.20 11 -class_Power_Opower(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_power__Suc_0) # label(axiom). [assumption].
% 1.94/2.20 12 -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].
% 1.94/2.20 13 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(B,tc_nat)) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff__number__of_1) # label(axiom). [assumption].
% 1.94/2.20 14 -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].
% 1.94/2.20 15 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat)) = c_HOL_Ozero__class_Ozero(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__eq__0__iff__number__of_2) # label(axiom). [assumption].
% 1.94/2.20 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(1,a,2,a)].
% 1.94/2.20 Derived: c_Power_Opower__class_Opower(tc_nat) = c_Power_Opower_Opower(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(tc_nat),tc_nat). [resolve(1,a,3,a)].
% 1.94/2.20 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_nat) | -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(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(1,a,4,d)].
% 1.94/2.20 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_nat) | -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(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(1,a,6,d)].
% 1.94/2.20 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_nat) | -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(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(1,a,7,d)].
% 1.94/2.21 Derived: -class_Ring__and__Field_Osemiring__0(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(1,a,8,b)].
% 1.94/2.21 Derived: -class_Ring__and__Field_Osemiring__0(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(1,a,9,b)].
% 1.94/2.21 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(1,a,11,a)].
% 1.94/2.21 Derived: -class_Ring__and__Field_Osemiring__0(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(1,a,12,b)].
% 1.94/2.21 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_nat) | -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(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(1,a,13,d)].
% 1.94/2.21 16 class_Power_Opower(tc_Int_Oint) # label(clsarity_Int__Oint__Power_Opower) # label(axiom). [assumption].
% 1.94/2.21 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(16,a,2,a)].
% 1.94/2.21 Derived: c_Power_Opower__class_Opower(tc_Int_Oint) = c_Power_Opower_Opower(c_HOL_Oone__class_Oone(tc_Int_Oint),c_HOL_Otimes__class_Otimes(tc_Int_Oint),tc_Int_Oint). [resolve(16,a,3,a)].
% 1.94/2.21 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) | -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(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(16,a,4,d)].
% 1.94/2.21 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) | -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(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(16,a,6,d)].
% 1.94/2.21 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) | -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(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(16,a,7,d)].
% 1.94/2.21 Derived: -class_Ring__and__Field_Osemiring__0(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(16,a,8,b)].
% 1.94/2.21 Derived: -class_Ring__and__Field_Osemiring__0(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(16,a,9,b)].
% 1.94/2.21 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(16,a,11,a)].
% 1.94/2.21 Derived: -class_Ring__and__Field_Osemiring__0(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(16,a,12,b)].
% 1.94/2.21 Derived: -class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) | -class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) | -class_Ring__and__Field_Omult__zero(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(16,a,13,d)].
% 2.07/2.30 17 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 2.07/2.30 18 -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].
% 2.07/2.30 19 -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].
% 2.07/2.30 20 -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].
% 2.07/2.30 21 -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].
% 2.07/2.30 22 -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].
% 2.07/2.30 23 -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].
% 2.07/2.30 24 -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].
% 2.07/2.30 25 -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].
% 2.07/2.30 26 -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].
% 2.07/2.30 27 -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].
% 2.07/2.30 28 -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].
% 2.07/2.30 29 -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].
% 2.07/2.30 30 -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].
% 2.07/2.30 31 -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].
% 2.07/2.30 32 -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].
% 2.07/2.30 33 -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].
% 2.07/2.30 34 -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].
% 2.07/2.30 35 -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].
% 2.07/2.30 36 -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].
% 2.07/2.30 37 -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].
% 2.07/2.30 38 -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].
% 2.07/2.30 39 -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].
% 2.07/2.30 40 -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].
% 2.07/2.30 41 -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].
% 2.07/2.30 42 -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].
% 2.07/2.30 43 -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].
% 2.07/2.30 44 -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].
% 2.07/2.30 45 -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].
% 2.07/2.30 46 -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].
% 2.07/2.30 47 -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].
% 2.07/2.30 48 -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].
% 2.07/2.30 49 -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].
% 2.07/2.30 50 -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].
% 2.07/2.30 51 -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].
% 2.07/2.30 52 -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].
% 2.07/2.30 53 -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].
% 2.07/2.30 54 -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].
% 2.07/2.30 55 -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].
% 2.07/2.30 56 -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].
% 2.07/2.30 57 -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].
% 2.07/2.30 58 -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].
% 2.07/2.30 59 -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].
% 2.07/2.30 60 -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].
% 2.07/2.30 61 -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].
% 2.07/2.30 62 -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].
% 2.07/2.30 63 -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].
% 2.07/2.30 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(17,a,19,a)].
% 2.07/2.30 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(17,a,20,a)].
% 2.07/2.30 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(17,a,21,a)].
% 2.07/2.30 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(17,a,23,a)].
% 2.07/2.30 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(17,a,24,a)].
% 2.07/2.30 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(17,a,25,a)].
% 2.07/2.30 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(17,a,26,a)].
% 2.07/2.30 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(17,a,27,a)].
% 2.07/2.30 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(17,a,29,a)].
% 2.07/2.30 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(17,a,30,a)].
% 2.07/2.31 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(17,a,31,a)].
% 2.07/2.31 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(17,a,32,a)].
% 2.07/2.31 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(17,a,33,a)].
% 2.07/2.31 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(17,a,34,a)].
% 2.07/2.31 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(17,a,36,a)].
% 2.07/2.31 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(17,a,37,a)].
% 2.07/2.31 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(17,a,38,a)].
% 2.07/2.31 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(17,a,39,a)].
% 2.07/2.31 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = A. [resolve(17,a,40,a)].
% 2.07/2.31 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(17,a,41,a)].
% 2.07/2.31 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(17,a,45,a)].
% 2.07/2.31 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(17,a,46,a)].
% 2.07/2.31 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(17,a,47,a)].
% 2.07/2.31 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(17,a,48,a)].
% 2.07/2.31 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(17,a,49,a)].
% 2.07/2.31 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(17,a,50,a)].
% 2.07/2.31 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(17,a,51,a)].
% 2.07/2.31 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(17,a,52,a)].
% 2.07/2.31 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(17,a,54,a)].
% 2.07/2.31 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(17,a,55,a)].
% 2.07/2.31 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(17,a,57,a)].
% 2.07/2.31 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(17,a,58,a)].
% 2.07/2.31 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(17,a,61,a)].
% 2.07/2.31 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(17,a,62,a)].
% 2.07/2.31 64 class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 2.07/2.31 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(64,a,19,a)].
% 2.07/2.31 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(64,a,20,a)].
% 2.07/2.31 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(64,a,21,a)].
% 2.07/2.31 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(64,a,23,a)].
% 2.07/2.31 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(64,a,24,a)].
% 2.07/2.31 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(64,a,25,a)].
% 2.07/2.31 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(64,a,26,a)].
% 2.07/2.31 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(64,a,27,a)].
% 2.07/2.31 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(64,a,29,a)].
% 2.07/2.31 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(64,a,30,a)].
% 2.07/2.31 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(64,a,31,a)].
% 2.07/2.31 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(64,a,32,a)].
% 2.07/2.31 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A) = A. [resolve(64,a,33,a)].
% 2.07/2.31 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)) = A. [resolve(64,a,34,a)].
% 2.07/2.31 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(64,a,36,a)].
% 2.07/2.31 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(64,a,37,a)].
% 2.07/2.31 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(64,a,38,a)].
% 2.07/2.31 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(64,a,39,a)].
% 2.07/2.31 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint)),A) = A. [resolve(64,a,40,a)].
% 2.07/2.31 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint)) = A. [resolve(64,a,41,a)].
% 2.07/2.31 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(64,a,45,a)].
% 2.07/2.31 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(64,a,46,a)].
% 2.07/2.31 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(64,a,47,a)].
% 2.07/2.31 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(64,a,48,a)].
% 2.07/2.31 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(64,a,49,a)].
% 2.07/2.31 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(64,a,50,a)].
% 2.07/2.31 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(64,a,51,a)].
% 2.27/2.50 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(64,a,52,a)].
% 2.27/2.50 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(64,a,54,a)].
% 2.27/2.50 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(64,a,55,a)].
% 2.27/2.50 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(64,a,57,a)].
% 2.27/2.50 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(64,a,58,a)].
% 2.27/2.50 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(64,a,61,a)].
% 2.27/2.50 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(64,a,62,a)].
% 2.27/2.50 65 class_Divides_Osemiring__div(tc_nat) # label(clsarity_nat__Divides_Osemiring__div) # label(axiom). [assumption].
% 2.27/2.50 66 -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].
% 2.27/2.50 67 -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].
% 2.27/2.50 68 -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].
% 2.27/2.50 69 -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].
% 2.27/2.50 70 -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].
% 2.27/2.50 71 -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].
% 2.27/2.50 72 -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].
% 2.27/2.50 73 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),B,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Odiv(C,B,A)),c_HOL_Oone__class_Oone(A)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__add__self1_0) # label(axiom). [assumption].
% 2.27/2.50 74 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),C,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Odiv(B,C,A)),c_HOL_Oone__class_Oone(A)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__add__self2_0) # label(axiom). [assumption].
% 2.27/2.50 75 -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].
% 2.27/2.50 76 -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].
% 2.27/2.50 77 -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].
% 2.27/2.50 78 -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].
% 2.27/2.50 79 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,B,A) = c_HOL_Oone__class_Oone(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__self_0) # label(axiom). [assumption].
% 2.27/2.50 80 -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].
% 2.27/2.50 81 -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].
% 2.27/2.50 82 -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].
% 2.27/2.50 83 -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].
% 2.27/2.50 84 -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].
% 2.27/2.50 85 -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].
% 2.27/2.50 86 -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].
% 2.27/2.50 87 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Oone__class_Oone(A),A) = B # label(cls_div__by__1_0) # label(axiom). [assumption].
% 2.27/2.50 88 -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].
% 2.27/2.50 89 -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].
% 2.27/2.50 90 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__by__0_0) # label(axiom). [assumption].
% 2.27/2.50 91 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__0_0) # label(axiom). [assumption].
% 2.27/2.50 92 -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].
% 2.27/2.50 93 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),C,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),c_Divides_Odiv__class_Odiv(B,C,A)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self2_0) # label(axiom). [assumption].
% 2.27/2.50 94 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)),D,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),c_Divides_Odiv__class_Odiv(B,D,A)) | D = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self1_0) # label(axiom). [assumption].
% 2.27/2.50 95 -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].
% 2.27/2.50 96 -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].
% 2.27/2.50 97 -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].
% 2.27/2.50 98 -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].
% 2.27/2.50 99 -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].
% 2.27/2.50 100 -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].
% 2.27/2.50 101 -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].
% 2.27/2.50 102 -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].
% 2.27/2.50 103 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),B,A) = C | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self1__is__id_0) # label(axiom). [assumption].
% 2.27/2.50 104 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),C,A) = B | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__self2__is__id_0) # label(axiom). [assumption].
% 2.27/2.50 105 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),C),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult1__if_0) # label(axiom). [assumption].
% 2.27/2.50 106 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A) = c_Divides_Odiv__class_Odiv(C,D,A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult1_0) # label(axiom). [assumption].
% 2.27/2.50 107 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A) = c_Divides_Odiv__class_Odiv(B,D,A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_div__mult__mult2_0) # label(axiom). [assumption].
% 2.27/2.50 108 -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].
% 2.27/2.50 109 -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].
% 2.27/2.50 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(65,a,66,a)].
% 2.27/2.50 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(65,a,67,a)].
% 2.27/2.50 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(65,a,68,a)].
% 2.27/2.50 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(65,a,69,a)].
% 2.27/2.50 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(65,a,70,a)].
% 2.27/2.50 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(65,a,71,a)].
% 2.27/2.50 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(65,a,72,a)].
% 2.27/2.50 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(65,a,73,a)].
% 2.27/2.50 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(65,a,74,a)].
% 2.27/2.50 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(65,a,75,a)].
% 2.27/2.50 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(65,a,76,a)].
% 2.27/2.50 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(65,a,77,a)].
% 2.27/2.50 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(65,a,78,a)].
% 2.27/2.50 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(65,a,79,a)].
% 2.27/2.50 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(65,a,80,a)].
% 2.27/2.50 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(65,a,81,a)].
% 2.27/2.50 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(65,a,82,a)].
% 2.27/2.50 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(65,a,83,a)].
% 2.27/2.50 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(65,a,84,a)].
% 2.27/2.50 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(65,a,85,a)].
% 2.27/2.50 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(65,a,86,a)].
% 2.27/2.50 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = A. [resolve(65,a,87,a)].
% 2.27/2.50 Derived: c_Divides_Odiv__class_Omod(A,A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(65,a,88,a)].
% 2.27/2.50 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A. [resolve(65,a,89,a)].
% 2.27/2.50 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(65,a,90,a)].
% 2.27/2.50 Derived: c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(65,a,91,a)].
% 2.27/2.50 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(65,a,92,a)].
% 2.27/2.50 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(65,a,93,a)].
% 2.27/2.50 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(65,a,94,a)].
% 2.27/2.50 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(65,a,95,a)].
% 2.27/2.50 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(65,a,96,a)].
% 2.27/2.50 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(65,a,97,a)].
% 2.27/2.50 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(65,a,98,a)].
% 2.27/2.50 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(65,a,99,a)].
% 2.27/2.50 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(65,a,100,a)].
% 2.27/2.50 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(65,a,101,a)].
% 2.27/2.50 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(65,a,102,a)].
% 2.27/2.50 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(65,a,103,a)].
% 2.27/2.50 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(65,a,104,a)].
% 2.27/2.50 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(65,a,105,a)].
% 2.27/2.50 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(65,a,106,a)].
% 2.27/2.50 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(65,a,107,a)].
% 2.27/2.50 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(65,a,108,a)].
% 2.27/2.50 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(65,a,109,a)].
% 2.27/2.50 110 class_Divides_Osemiring__div(tc_Int_Oint) # label(clsarity_Int__Oint__Divides_Osemiring__div) # label(axiom). [assumption].
% 2.27/2.50 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(110,a,66,a)].
% 2.27/2.50 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(110,a,67,a)].
% 2.27/2.50 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(110,a,68,a)].
% 2.27/2.50 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(110,a,69,a)].
% 2.27/2.50 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(110,a,70,a)].
% 2.27/2.50 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(110,a,71,a)].
% 2.27/2.50 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(110,a,72,a)].
% 2.27/2.50 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(110,a,73,a)].
% 2.27/2.50 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(110,a,74,a)].
% 2.27/2.50 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(110,a,75,a)].
% 2.27/2.50 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(110,a,76,a)].
% 2.27/2.50 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(110,a,77,a)].
% 2.27/2.50 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(110,a,78,a)].
% 2.27/2.50 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(110,a,79,a)].
% 2.27/2.50 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(110,a,80,a)].
% 2.27/2.50 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(110,a,81,a)].
% 2.27/2.50 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(110,a,82,a)].
% 2.27/2.50 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(110,a,83,a)].
% 2.27/2.50 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(110,a,84,a)].
% 2.27/2.50 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(110,a,85,a)].
% 2.27/2.50 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(110,a,86,a)].
% 2.27/2.50 Derived: c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) = A. [resolve(110,a,87,a)].
% 2.27/2.50 Derived: c_Divides_Odiv__class_Omod(A,A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(110,a,88,a)].
% 2.27/2.50 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = A. [resolve(110,a,89,a)].
% 2.27/2.50 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(110,a,90,a)].
% 2.27/2.50 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(110,a,91,a)].
% 2.27/2.50 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(110,a,92,a)].
% 2.27/2.50 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(110,a,93,a)].
% 2.27/2.50 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(110,a,94,a)].
% 2.27/2.50 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(110,a,95,a)].
% 2.27/2.50 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(110,a,96,a)].
% 2.27/2.50 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(110,a,97,a)].
% 2.27/2.50 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(110,a,98,a)].
% 2.27/2.50 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(110,a,99,a)].
% 2.27/2.50 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(110,a,100,a)].
% 2.27/2.50 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(110,a,101,a)].
% 2.27/2.50 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(110,a,102,a)].
% 2.27/2.50 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(110,a,103,a)].
% 2.27/2.50 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(110,a,104,a)].
% 2.27/2.50 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(110,a,105,a)].
% 2.32/2.60 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(110,a,106,a)].
% 2.32/2.60 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(110,a,107,a)].
% 2.32/2.60 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(110,a,108,a)].
% 2.32/2.60 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(110,a,109,a)].
% 2.32/2.60 111 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 2.32/2.60 112 -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].
% 2.32/2.60 113 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,hAPP(c_Suc,D),tc_nat),tc_nat,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat),tc_nat,A)),hAPP(B,D)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(D,tc_nat),C)) # label(cls_setsum__op__ivl__Suc_1) # label(axiom). [assumption].
% 2.32/2.60 114 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat),tc_nat,A)),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(D,E,tc_nat),tc_nat,A)) = c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,E,tc_nat),tc_nat,A) | -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].
% 2.32/2.60 115 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat),tc_nat,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,C)),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,C),D,tc_nat),tc_nat,A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),D)) # label(cls_setsum__head__upt__Suc_0) # label(axiom). [assumption].
% 2.32/2.60 116 -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].
% 2.32/2.60 117 -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].
% 2.32/2.60 118 -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].
% 2.32/2.60 119 -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].
% 2.32/2.60 120 -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].
% 2.32/2.60 121 -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].
% 2.32/2.60 122 -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].
% 2.32/2.60 123 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_lessequals(B,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_add__strict__increasing_0) # label(axiom). [assumption].
% 2.32/2.60 124 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_add__strict__increasing2_0) # label(axiom). [assumption].
% 2.32/2.60 125 -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].
% 2.32/2.60 126 -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].
% 2.32/2.60 127 -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].
% 2.32/2.60 128 -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].
% 2.32/2.60 129 -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].
% 2.32/2.60 130 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,hAPP(c_Suc,D),tc_nat),tc_nat,A) = c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,tc_nat),C)) # label(cls_setsum__op__ivl__Suc_0) # label(axiom). [assumption].
% 2.32/2.60 131 -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].
% 2.32/2.60 132 -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].
% 2.32/2.60 133 -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].
% 2.32/2.60 134 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_setsum__empty_0) # label(axiom). [assumption].
% 2.32/2.60 135 -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].
% 2.32/2.60 136 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat,A) = 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].
% 2.32/2.60 137 -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].
% 2.32/2.60 138 -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].
% 2.32/2.60 139 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,C),hAPP(c_Suc,D),tc_nat),tc_nat,A) = c_Finite__Set_Osetsum(c_COMBB(B,c_Suc,tc_nat,A,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat),tc_nat,A) # label(cls_setsum__shift__bounds__Suc__ivl_0) # label(axiom). [assumption].
% 2.32/2.60 140 -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].
% 2.32/2.60 141 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(A) | c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),C,tc_nat),tc_nat,A) = c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,A) # label(cls_setsum__shift__lb__Suc0__0__upt_0) # label(axiom). [assumption].
% 2.32/2.60 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat),tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,tc_nat)),hAPP(A,C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(111,a,113,a)].
% 2.32/2.60 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,tc_nat)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat),tc_nat,tc_nat)) = c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat),tc_nat,tc_nat) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(111,a,114,a)].
% 2.32/2.60 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(A,B)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),C,tc_nat),tc_nat,tc_nat)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(111,a,115,a)].
% 2.32/2.60 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(111,a,116,b)].
% 2.32/2.60 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(111,a,117,b)].
% 2.32/2.60 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(111,a,118,a)].
% 2.32/2.60 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(111,a,121,a)].
% 2.32/2.60 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(111,a,122,a)].
% 2.32/2.60 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(111,a,123,b)].
% 2.32/2.60 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(111,a,124,b)].
% 2.32/2.60 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(111,a,126,a)].
% 2.32/2.60 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(111,a,129,a)].
% 2.32/2.60 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat),tc_nat,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(111,a,130,a)].
% 2.32/2.60 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(111,a,131,a)].
% 2.32/2.60 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(111,a,132,a)].
% 2.32/2.60 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(111,a,133,a)].
% 2.32/2.60 Derived: c_Finite__Set_Osetsum(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(111,a,134,a)].
% 2.32/2.60 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(111,a,135,a)].
% 2.32/2.60 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat,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(111,a,136,a)].
% 2.32/2.60 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(111,a,137,a)].
% 2.32/2.60 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(111,a,138,a)].
% 2.32/2.60 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),hAPP(c_Suc,C),tc_nat),tc_nat,tc_nat) = c_Finite__Set_Osetsum(c_COMBB(A,c_Suc,tc_nat,tc_nat,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,tc_nat). [resolve(111,a,139,a)].
% 2.32/2.60 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(111,a,140,a)].
% 2.32/2.60 Derived: hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_nat) | c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),B,tc_nat),tc_nat,tc_nat) = c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat,tc_nat). [resolve(111,a,141,a)].
% 2.32/2.60 142 class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 2.32/2.60 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat),tc_nat,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,tc_Int_Oint)),hAPP(A,C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(142,a,113,a)].
% 2.32/2.60 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,tc_Int_Oint)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat),tc_nat,tc_Int_Oint)) = c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat),tc_nat,tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(C,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)). [resolve(142,a,114,a)].
% 2.32/2.60 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(A,B)),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),C,tc_nat),tc_nat,tc_Int_Oint)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(142,a,115,a)].
% 2.32/2.60 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(142,a,116,b)].
% 2.32/2.60 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(142,a,117,b)].
% 2.32/2.60 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(142,a,118,a)].
% 2.32/2.60 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(142,a,121,a)].
% 2.32/2.60 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(142,a,122,a)].
% 2.32/2.60 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(142,a,123,b)].
% 2.32/2.61 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(142,a,124,b)].
% 2.32/2.61 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(142,a,126,a)].
% 2.32/2.61 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(142,a,129,a)].
% 2.32/2.61 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,hAPP(c_Suc,C),tc_nat),tc_nat,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(142,a,130,a)].
% 2.32/2.61 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(142,a,131,a)].
% 2.32/2.61 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(142,a,132,a)].
% 2.32/2.61 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(142,a,133,a)].
% 2.32/2.61 Derived: c_Finite__Set_Osetsum(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(142,a,134,a)].
% 2.32/2.61 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(142,a,135,a)].
% 2.32/2.61 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat,tc_Int_Oint) = 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(142,a,136,a)].
% 2.32/2.61 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(142,a,137,a)].
% 2.32/2.61 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(142,a,138,a)].
% 2.47/2.72 Derived: c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,B),hAPP(c_Suc,C),tc_nat),tc_nat,tc_Int_Oint) = c_Finite__Set_Osetsum(c_COMBB(A,c_Suc,tc_nat,tc_Int_Oint,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,tc_Int_Oint). [resolve(142,a,139,a)].
% 2.47/2.72 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(142,a,140,a)].
% 2.47/2.72 Derived: hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),B,tc_nat),tc_nat,tc_Int_Oint) = c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat,tc_Int_Oint). [resolve(142,a,141,a)].
% 2.47/2.72 143 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 2.47/2.72 144 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_pos__add__strict_0) # label(axiom). [assumption].
% 2.47/2.72 145 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__less__power__Suc_0) # label(axiom). [assumption].
% 2.47/2.72 146 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A)))) # label(cls_less__add__one_0) # label(axiom). [assumption].
% 2.47/2.72 147 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__gt1__lemma_0) # label(axiom). [assumption].
% 2.47/2.72 148 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),D))) # label(cls_power__less__imp__less__base_0) # label(axiom). [assumption].
% 2.47/2.72 149 -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(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__le__imp__le__exp_0) # label(axiom). [assumption].
% 2.47/2.72 150 -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(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__increasing__iff_0) # label(axiom). [assumption].
% 2.47/2.73 151 -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(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__increasing__iff_1) # label(axiom). [assumption].
% 2.47/2.73 152 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),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].
% 2.47/2.73 153 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__Suc__less_0) # label(axiom). [assumption].
% 2.47/2.73 154 -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].
% 2.47/2.73 155 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)),A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_power__Suc__less__one_0) # label(axiom). [assumption].
% 2.47/2.73 156 -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].
% 2.47/2.73 157 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_one__less__power_0) # label(axiom). [assumption].
% 2.47/2.73 158 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_power__strict__mono_0) # label(axiom). [assumption].
% 2.47/2.73 159 -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(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),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].
% 2.47/2.73 160 -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].
% 2.47/2.73 161 -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].
% 2.47/2.73 162 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,tc_nat),C)) # label(cls_power__strict__decreasing_0) # label(axiom). [assumption].
% 2.47/2.73 163 -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].
% 2.47/2.73 164 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__less__power_0) # label(axiom). [assumption].
% 2.47/2.73 165 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__one__less__zero_0) # label(axiom). [assumption].
% 2.47/2.73 166 -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].
% 2.47/2.73 167 -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].
% 2.47/2.73 168 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_less__1__mult_0) # label(axiom). [assumption].
% 2.47/2.73 169 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__gt1_0) # label(axiom). [assumption].
% 2.47/2.73 170 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Oone__class_Oone(A))) # label(cls_zero__less__one_0) # label(axiom). [assumption].
% 2.47/2.73 171 -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(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) | C = D # label(cls_power__inject__exp_0) # label(axiom). [assumption].
% 2.47/2.73 172 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__less__imp__less__exp_0) # label(axiom). [assumption].
% 2.47/2.73 173 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),D)) # label(cls_power__strict__increasing_0) # label(axiom). [assumption].
% 2.47/2.73 174 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),D)) # label(cls_power__strict__increasing__iff_0) # label(axiom). [assumption].
% 2.47/2.73 175 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),B)) # label(cls_power__strict__increasing__iff_1) # label(axiom). [assumption].
% 2.47/2.73 176 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),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__less__imp__less_0) # label(axiom). [assumption].
% 2.47/2.73 177 -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].
% 2.47/2.73 178 -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].
% 2.47/2.73 179 -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].
% 2.47/2.73 180 -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].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(143,a,144,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B),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(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(143,a,145,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)))). [resolve(143,a,146,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),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(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(143,a,147,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),C),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),B),C))). [resolve(143,a,148,a)].
% 2.47/2.73 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(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),C)). [resolve(143,a,149,a)].
% 2.47/2.73 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(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(143,a,151,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),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(143,a,152,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B)),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(143,a,153,a)].
% 2.47/2.73 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(143,a,154,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B)),tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(143,a,155,a)].
% 2.47/2.73 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(143,a,156,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(143,a,157,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(143,a,158,a)].
% 2.47/2.73 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(c_HOL_Oord__class_Oless(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(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(143,a,159,a)].
% 2.47/2.73 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(143,a,160,a)].
% 2.47/2.73 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(143,a,161,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Oone__class_Oone(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(143,a,162,a)].
% 2.47/2.73 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(143,a,163,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(143,a,164,a)].
% 2.47/2.73 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(143,a,165,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat))). [resolve(143,a,166,a)].
% 2.47/2.73 Derived: -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(143,a,167,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(143,a,168,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),hAPP(c_Suc,B)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)). [resolve(143,a,169,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat))). [resolve(143,a,170,a)].
% 2.47/2.73 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(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)) | B = C. [resolve(143,a,171,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(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(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),C)). [resolve(143,a,172,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(143,a,173,a)].
% 2.47/2.73 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(143,a,177,a)].
% 2.47/2.73 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(143,a,178,a)].
% 2.47/2.73 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(143,a,179,a)].
% 2.47/2.73 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(143,a,180,a)].
% 2.47/2.73 181 class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(181,a,144,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),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(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(181,a,145,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Oone__class_Oone(tc_Int_Oint)))). [resolve(181,a,146,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),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(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(181,a,147,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),C),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),C))). [resolve(181,a,148,a)].
% 2.47/2.73 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(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),C)). [resolve(181,a,149,a)].
% 2.47/2.73 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(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(181,a,151,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),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(181,a,152,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B)),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(181,a,153,a)].
% 2.47/2.73 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(181,a,154,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Suc,B)),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(181,a,155,a)].
% 2.47/2.73 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(181,a,156,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(181,a,157,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(181,a,158,a)].
% 2.47/2.73 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(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),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(181,a,159,a)].
% 2.47/2.73 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(181,a,160,a)].
% 2.47/2.73 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(181,a,161,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_nat),B)). [resolve(181,a,162,a)].
% 2.47/2.73 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(181,a,163,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(181,a,164,a)].
% 2.47/2.73 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(181,a,165,a)].
% 2.47/2.73 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(181,a,166,a)].
% 2.47/2.73 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(181,a,167,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(181,a,168,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Suc,B)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)). [resolve(181,a,169,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))). [resolve(181,a,170,a)].
% 2.47/2.73 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(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)) | B = C. [resolve(181,a,171,a)].
% 2.47/2.73 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(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(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),C)). [resolve(181,a,172,a)].
% 2.74/3.00 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(181,a,173,a)].
% 2.74/3.00 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(181,a,177,a)].
% 2.74/3.00 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(181,a,178,a)].
% 2.74/3.00 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(181,a,179,a)].
% 2.74/3.00 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(181,a,180,a)].
% 2.74/3.00 182 class_Ring__and__Field_Oordered__idom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__idom) # label(axiom). [assumption].
% 2.74/3.00 183 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) | C = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__le__zero__eq_4) # label(axiom). [assumption].
% 2.74/3.00 184 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_power__less__zero__eq_2) # label(axiom). [assumption].
% 2.74/3.00 185 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | C = B # label(cls_linorder__neqE__ordered__idom_0) # label(axiom). [assumption].
% 2.74/3.00 186 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),A),c_Int_Onumber__class_Onumber__of(C,A))) # label(cls_le__number__of_0) # label(axiom). [assumption].
% 2.74/3.00 187 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),A),c_Int_Onumber__class_Onumber__of(C,A))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),C)) # label(cls_le__number__of_1) # label(axiom). [assumption].
% 2.74/3.00 188 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_even__less__0__iff_0) # label(axiom). [assumption].
% 2.74/3.00 189 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_even__less__0__iff_1) # label(axiom). [assumption].
% 2.74/3.00 190 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)))) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_zero__le__power__eq__number__of_2) # label(axiom). [assumption].
% 2.74/3.00 191 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)))) # label(cls_zero__le__power__eq__number__of_0) # label(axiom). [assumption].
% 2.74/3.00 192 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq_1) # label(axiom). [assumption].
% 2.74/3.00 193 -class_Ring__and__Field_Oordered__idom(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(B,A),D)) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_power__mono__odd_0) # label(axiom). [assumption].
% 2.74/3.00 194 -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(B,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__less__zero__eq__number__of_0) # label(axiom). [assumption].
% 2.74/3.00 195 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B))) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) # label(cls_zero__less__power__eq_1) # label(axiom). [assumption].
% 2.74/3.00 196 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__less__power__eq_5) # label(axiom). [assumption].
% 2.74/3.00 197 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),A),c_Int_Onumber__class_Onumber__of(C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),C)) # label(cls_less__number__of_1) # label(axiom). [assumption].
% 2.74/3.00 198 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),A),c_Int_Onumber__class_Onumber__of(C,A))) # label(cls_less__number__of_0) # label(axiom). [assumption].
% 2.74/3.00 199 -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__less__zero__eq_0) # label(axiom). [assumption].
% 2.74/3.00 200 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) | C = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) # label(cls_zero__less__power__eq_0) # label(axiom). [assumption].
% 2.74/3.00 201 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_power__less__zero__eq__number__of_2) # label(axiom). [assumption].
% 2.74/3.00 202 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) | B = c_HOL_Ozero__class_Ozero(A) | -c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__less__power__eq_4) # label(axiom). [assumption].
% 2.74/3.00 203 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)))) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_zero__le__power__eq__number__of_1) # label(axiom). [assumption].
% 2.74/3.00 204 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq__number__of_1) # label(axiom). [assumption].
% 2.74/3.00 205 -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq_5) # label(axiom). [assumption].
% 2.74/3.00 206 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__less__zero__eq_1) # label(axiom). [assumption].
% 2.74/3.00 207 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq_3) # label(axiom). [assumption].
% 2.74/3.00 208 -class_Ring__and__Field_Oordered__idom(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__power__eq_1) # label(axiom). [assumption].
% 2.74/3.00 209 -class_Ring__and__Field_Oordered__idom(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__power__iff_2) # label(axiom). [assumption].
% 2.74/3.00 210 -class_Ring__and__Field_Oordered__idom(A) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(B,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq__number__of_2) # label(axiom). [assumption].
% 2.74/3.00 211 -class_Ring__and__Field_Oordered__idom(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__iff_1) # label(axiom). [assumption].
% 2.74/3.00 212 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),B)) | -hBOOL(hAPP(c_lessequals(C,A),c_HOL_Oone__class_Oone(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)) # label(cls_mult__right__le__one__le_0) # label(axiom). [assumption].
% 2.74/3.00 213 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),C)) | -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(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__left__le__one__le_0) # label(axiom). [assumption].
% 2.74/3.00 214 -class_Ring__and__Field_Oordered__idom(A) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | hBOOL(hAPP(c_lessequals(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq_2) # label(axiom). [assumption].
% 2.74/3.00 215 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_zero__less__power__eq__number__of_5) # label(axiom). [assumption].
% 2.74/3.00 216 -class_Ring__and__Field_Oordered__idom(A) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Ozero__class_Ozero(tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq_0) # label(axiom). [assumption].
% 2.74/3.00 217 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)))) | B = c_HOL_Ozero__class_Ozero(A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) # label(cls_zero__less__power__eq__number__of_4) # label(axiom). [assumption].
% 2.74/3.00 218 -class_Ring__and__Field_Oordered__idom(A) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),B))) # label(cls_zero__le__power__iff_0) # label(axiom). [assumption].
% 2.74/3.00 219 -class_Ring__and__Field_Oordered__idom(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)) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__odd__power_1) # label(axiom). [assumption].
% 2.74/3.00 220 -class_Ring__and__Field_Oordered__idom(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_Power_Opower__class_Opower(A),B),C))) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__odd__power_0) # label(axiom). [assumption].
% 2.74/3.00 221 -class_Ring__and__Field_Oordered__idom(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)) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) # label(cls_zero__le__power__eq_2) # label(axiom). [assumption].
% 2.74/3.00 222 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(C,tc_nat) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C))) # label(cls_zero__le__power__eq_0) # label(axiom). [assumption].
% 2.74/3.00 223 -class_Ring__and__Field_Oordered__idom(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__sum__power2__lt__zero_0) # label(axiom). [assumption].
% 2.74/3.00 224 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),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))))) # label(cls_sum__power2__ge__zero_0) # label(axiom). [assumption].
% 2.74/3.00 225 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),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))))) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__power2__gt__zero__iff_1) # label(axiom). [assumption].
% 2.74/3.00 226 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))))) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__power2__gt__zero__iff_2) # label(axiom). [assumption].
% 2.74/3.00 227 -class_Ring__and__Field_Oordered__idom(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))))) # label(cls_sum__power2__gt__zero__iff_0) # label(axiom). [assumption].
% 2.74/3.00 228 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_sum__power2__le__zero__iff_2) # label(axiom). [assumption].
% 2.74/3.00 229 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_sum__power2__le__zero__iff_0) # label(axiom). [assumption].
% 2.74/3.00 230 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_sum__power2__le__zero__iff_1) # label(axiom). [assumption].
% 2.74/3.00 231 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Ozero__class_Ozero(tc_nat)))) # label(cls_zero__less__power__eq_3) # label(axiom). [assumption].
% 2.74/3.00 232 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),B))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_zero__less__power__eq_2) # label(axiom). [assumption].
% 2.74/3.00 233 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq__number__of_3) # label(axiom). [assumption].
% 2.74/3.00 234 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__less__zero__eq__number__of_1) # label(axiom). [assumption].
% 2.74/3.00 235 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),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_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) # label(cls_zero__less__power__eq__number__of_1) # label(axiom). [assumption].
% 2.74/3.00 236 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) | c_Int_Onumber__class_Onumber__of(C,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)))) # label(cls_zero__less__power__eq__number__of_0) # label(axiom). [assumption].
% 2.74/3.00 237 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,A),c_HOL_Ozero__class_Ozero(A))) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat) | c_Int_Onumber__class_Onumber__of(C,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__le__zero__eq__number__of_4) # label(axiom). [assumption].
% 2.74/3.00 238 -class_Ring__and__Field_Oordered__idom(A) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq__number__of_5) # label(axiom). [assumption].
% 2.74/3.00 239 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_Int_OBit1(c_Int_OPls))) # label(cls_less__special_I4_J_1) # label(axiom). [assumption].
% 2.74/3.00 240 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_Int_OBit1(c_Int_OPls))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),A),c_HOL_Oone__class_Oone(A))) # label(cls_less__special_I4_J_0) # label(axiom). [assumption].
% 2.74/3.00 241 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),A),c_HOL_Oone__class_Oone(A))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_Int_OBit1(c_Int_OPls))) # label(cls_le__special_I4_J_1) # label(axiom). [assumption].
% 2.74/3.00 242 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_Int_OBit1(c_Int_OPls))) | -hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),A),c_HOL_Oone__class_Oone(A))) # label(cls_le__special_I4_J_0) # label(axiom). [assumption].
% 2.74/3.00 243 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),c_Int_Onumber__class_Onumber__of(B,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_OBit1(c_Int_OPls),tc_Int_Oint),B)) # label(cls_less__special_I2_J_1) # label(axiom). [assumption].
% 2.74/3.00 244 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_OBit1(c_Int_OPls),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),A),c_Int_Onumber__class_Onumber__of(B,A))) # label(cls_less__special_I2_J_0) # label(axiom). [assumption].
% 2.74/3.00 245 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),c_Int_Onumber__class_Onumber__of(B,A))) | -hBOOL(hAPP(c_lessequals(c_Int_OBit1(c_Int_OPls),tc_Int_Oint),B)) # label(cls_le__special_I2_J_1) # label(axiom). [assumption].
% 2.74/3.00 246 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(c_lessequals(c_Int_OBit1(c_Int_OPls),tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(A),A),c_Int_Onumber__class_Onumber__of(B,A))) # label(cls_le__special_I2_J_0) # label(axiom). [assumption].
% 2.74/3.00 247 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),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)))) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_zero__less__power2_1) # label(axiom). [assumption].
% 2.74/3.00 248 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))) # label(cls_zero__le__power2_0) # label(axiom). [assumption].
% 2.74/3.00 249 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__power2__eq__zero__iff_0) # label(axiom). [assumption].
% 2.74/3.00 250 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__power2__eq__zero__iff_1) # label(axiom). [assumption].
% 2.74/3.00 251 -class_Ring__and__Field_Oordered__idom(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),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)))) # label(cls_zero__less__power2_0) # label(axiom). [assumption].
% 2.74/3.00 252 -class_Ring__and__Field_Oordered__idom(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power2__less__0_0) # label(axiom). [assumption].
% 2.74/3.00 253 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) = c_HOL_Ozero__class_Ozero(A) # label(cls_sum__power2__eq__zero__iff_2) # label(axiom). [assumption].
% 2.74/3.00 254 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_Int_OPls)) # label(cls_less__special_I3_J_1) # label(axiom). [assumption].
% 2.74/3.00 255 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),c_Int_OPls)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_less__special_I3_J_0) # label(axiom). [assumption].
% 2.74/3.00 256 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_Int_OPls)) # label(cls_le__special_I3_J_1) # label(axiom). [assumption].
% 2.74/3.00 257 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_Int_OPls)) | -hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_le__special_I3_J_0) # label(axiom). [assumption].
% 2.74/3.00 258 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_Int_Onumber__class_Onumber__of(B,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_OPls,tc_Int_Oint),B)) # label(cls_less__special_I1_J_1) # label(axiom). [assumption].
% 2.74/3.00 259 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_OPls,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_Int_Onumber__class_Onumber__of(B,A))) # label(cls_less__special_I1_J_0) # label(axiom). [assumption].
% 2.74/3.00 260 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_Int_Onumber__class_Onumber__of(B,A))) | -hBOOL(hAPP(c_lessequals(c_Int_OPls,tc_Int_Oint),B)) # label(cls_le__special_I1_J_1) # label(axiom). [assumption].
% 2.74/3.00 261 -class_Ring__and__Field_Oordered__idom(A) | -class_Int_Onumber__ring(A) | hBOOL(hAPP(c_lessequals(c_Int_OPls,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),c_Int_Onumber__class_Onumber__of(B,A))) # label(cls_le__special_I1_J_0) # label(axiom). [assumption].
% 2.74/3.00 262 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat)))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_zero__less__power__eq__number__of_2) # label(axiom). [assumption].
% 2.74/3.00 263 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(B,tc_nat)))) # label(cls_zero__less__power__eq__number__of_3) # label(axiom). [assumption].
% 2.74/3.00 264 -class_Ring__and__Field_Oordered__idom(A) | c_Int_Onumber__class_Onumber__of(B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(B,tc_nat)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_power__le__zero__eq__number__of_0) # label(axiom). [assumption].
% 2.74/3.00 265 -class_Ring__and__Field_Oordered__idom(A) | B = c_HOL_Ozero__class_Ozero(A) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C)),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_even__power__le__0__imp__0_0) # label(axiom). [assumption].
% 2.74/3.00 266 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),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)))) # label(cls_zero__le__even__power_H_0) # label(axiom). [assumption].
% 2.74/3.00 267 -class_Ring__and__Field_Oordered__idom(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_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))))) # label(cls_odd__0__le__power__imp__0__le_0) # label(axiom). [assumption].
% 2.74/3.00 268 -class_Ring__and__Field_Oordered__idom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),C))),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_odd__power__less__zero_0) # label(axiom). [assumption].
% 2.74/3.00 269 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_zero__eq__power2_0) # label(axiom). [assumption].
% 2.74/3.00 270 -class_Ring__and__Field_Oordered__idom(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) = c_HOL_Ozero__class_Ozero(A) # label(cls_zero__eq__power2_1) # label(axiom). [assumption].
% 2.74/3.00 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),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))) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(182,a,183,a)].
% 2.74/3.00 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(182,a,184,a)].
% 2.74/3.00 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),A)) | B = A. [resolve(182,a,185,a)].
% 2.74/3.00 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint))). [resolve(182,a,186,a)].
% 2.74/3.00 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(182,a,187,a)].
% 2.74/3.00 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(182,a,188,a)].
% 2.74/3.00 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(182,a,189,a)].
% 2.74/3.00 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat) | -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),c_Int_Onumber__class_Onumber__of(B,tc_nat)))). [resolve(182,a,191,a)].
% 2.74/3.00 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(182,a,192,a)].
% 2.74/3.00 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(A,tc_Int_Oint),C)) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(182,a,193,a)].
% 2.74/3.00 Derived: -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(A,tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(182,a,194,a)].
% 2.74/3.00 Derived: A = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A))) | -c_Parity_Oeven__odd__class_Oeven(A,tc_nat). [resolve(182,a,195,a)].
% 2.74/3.00 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)). [resolve(182,a,197,a)].
% 2.74/3.00 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint))). [resolve(182,a,198,a)].
% 2.74/3.00 Derived: -c_Parity_Oeven__odd__class_Oeven(A,tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(182,a,199,a)].
% 2.74/3.00 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | c_Parity_Oeven__odd__class_Oeven(B,tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))). [resolve(182,a,200,a)].
% 2.74/3.00 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B))) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(182,a,202,a)].
% 2.74/3.00 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),c_Int_Onumber__class_Onumber__of(B,tc_nat)))) | -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat). [resolve(182,a,203,a)].
% 2.74/3.00 Derived: -c_Parity_Oeven__odd__class_Oeven(A,tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(182,a,205,a)].
% 2.74/3.00 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(182,a,206,a)].
% 2.74/3.00 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),B),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(182,a,207,a)].
% 2.74/3.00 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))) | -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). [resolve(182,a,208,a)].
% 2.74/3.00 Derived: c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(A,tc_nat),tc_nat) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(A,tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(182,a,210,a)].
% 2.74/3.00 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(B,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),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(182,a,212,a)].
% 2.74/3.01 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B),tc_Int_Oint),B)) | -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_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)). [resolve(182,a,213,a)].
% 2.74/3.01 Derived: c_Parity_Oeven__odd__class_Oeven(A,tc_nat) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),A),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(182,a,214,a)].
% 2.74/3.01 Derived: -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(182,a,216,a)].
% 2.74/3.01 Derived: c_Parity_Oeven__odd__class_Oeven(A,tc_nat) | 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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),A))). [resolve(182,a,218,a)].
% 2.74/3.01 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(182,a,223,a)].
% 2.74/3.01 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),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))))). [resolve(182,a,224,a)].
% 2.74/3.01 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),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))))) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(182,a,225,a)].
% 2.74/3.01 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),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))))) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(182,a,226,a)].
% 2.74/3.01 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))))). [resolve(182,a,227,a)].
% 2.74/3.01 Derived: hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(182,a,228,a)].
% 2.74/3.01 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(182,a,229,a)].
% 2.74/3.01 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(182,a,230,a)].
% 2.74/3.01 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_nat)))). [resolve(182,a,231,a)].
% 2.74/3.01 Derived: A = c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),A))) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(182,a,232,a)].
% 2.74/3.01 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_Int_OBit1(c_Int_OPls))). [resolve(182,a,239,a)].
% 2.74/3.01 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_Int_OBit1(c_Int_OPls))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))). [resolve(182,a,240,a)].
% 2.74/3.01 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_Int_OBit1(c_Int_OPls))). [resolve(182,a,241,a)].
% 2.74/3.01 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_Int_OBit1(c_Int_OPls))) | -hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint),c_HOL_Oone__class_Oone(tc_Int_Oint))). [resolve(182,a,242,a)].
% 2.74/3.01 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_OBit1(c_Int_OPls),tc_Int_Oint),A)). [resolve(182,a,243,a)].
% 2.74/3.01 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_OBit1(c_Int_OPls),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint))). [resolve(182,a,244,a)].
% 2.74/3.01 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_Int_OBit1(c_Int_OPls),tc_Int_Oint),A)). [resolve(182,a,245,a)].
% 2.74/3.01 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(c_Int_OBit1(c_Int_OPls),tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint))). [resolve(182,a,246,a)].
% 2.74/3.01 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),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)))) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(182,a,247,a)].
% 2.74/3.01 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),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))). [resolve(182,a,248,a)].
% 2.74/3.01 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(182,a,249,a)].
% 2.74/3.01 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(182,a,250,a)].
% 2.74/3.01 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)))). [resolve(182,a,251,a)].
% 2.74/3.01 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(182,a,252,a)].
% 2.74/3.01 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(182,a,253,a)].
% 2.74/3.01 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_Int_OPls)). [resolve(182,a,254,a)].
% 2.74/3.01 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_Int_OPls)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(182,a,255,a)].
% 2.74/3.01 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_Int_OPls)). [resolve(182,a,256,a)].
% 2.74/3.01 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_Int_OPls)) | -hBOOL(hAPP(c_lessequals(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(182,a,257,a)].
% 2.74/3.01 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_OPls,tc_Int_Oint),A)). [resolve(182,a,258,a)].
% 2.74/3.01 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_OPls,tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint))). [resolve(182,a,259,a)].
% 2.74/3.01 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(c_Int_OPls,tc_Int_Oint),A)). [resolve(182,a,260,a)].
% 2.84/3.09 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hBOOL(hAPP(c_lessequals(c_Int_OPls,tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint))). [resolve(182,a,261,a)].
% 2.84/3.09 Derived: c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(A,tc_nat)))). [resolve(182,a,263,a)].
% 2.84/3.09 Derived: c_Int_Onumber__class_Onumber__of(A,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),B),c_Int_Onumber__class_Onumber__of(A,tc_nat)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(182,a,264,a)].
% 2.84/3.09 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(182,a,265,a)].
% 2.84/3.09 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),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B)))). [resolve(182,a,266,a)].
% 2.84/3.09 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_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))))). [resolve(182,a,267,a)].
% 2.84/3.09 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),hAPP(c_Suc,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),B))),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(182,a,268,a)].
% 2.84/3.09 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(182,a,269,a)].
% 2.84/3.09 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(182,a,270,a)].
% 2.84/3.09 271 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 2.84/3.09 272 -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].
% 2.84/3.09 273 -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].
% 2.84/3.09 274 -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].
% 2.84/3.09 275 -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].
% 2.84/3.09 276 -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].
% 2.84/3.09 277 -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].
% 2.84/3.09 278 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_Lattices_Oupper__semilattice__class_Osup(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_less__supI1_0) # label(axiom). [assumption].
% 2.84/3.09 279 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_Lattices_Oupper__semilattice__class_Osup(C,D,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_less__supI2_0) # label(axiom). [assumption].
% 2.84/3.09 280 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 2.84/3.09 281 -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].
% 2.84/3.09 282 -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].
% 2.84/3.09 283 -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].
% 2.84/3.09 284 -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].
% 2.84/3.09 285 -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].
% 2.84/3.09 286 -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].
% 2.84/3.09 287 -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].
% 2.84/3.09 288 -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].
% 2.84/3.09 289 -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].
% 2.84/3.09 290 -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].
% 2.84/3.09 291 -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].
% 2.84/3.09 292 -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].
% 2.84/3.09 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(271,a,272,a)].
% 2.84/3.09 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(271,a,273,a)].
% 2.84/3.09 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(271,a,274,a)].
% 2.84/3.09 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(271,a,275,a)].
% 2.84/3.09 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_fun(C,A)),c_Lattices_Oupper__semilattice__class_Osup(D,E,tc_fun(C,A)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_fun(C,A)),D)). [resolve(271,a,278,a)].
% 2.84/3.09 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_fun(C,A)),c_Lattices_Oupper__semilattice__class_Osup(D,E,tc_fun(C,A)))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_fun(C,A)),E)). [resolve(271,a,279,a)].
% 2.84/3.09 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(271,a,280,a)].
% 2.84/3.09 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(271,a,281,a)].
% 2.84/3.09 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(271,a,282,a)].
% 2.84/3.09 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(271,a,283,a)].
% 2.84/3.09 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(271,a,286,a)].
% 2.84/3.09 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(271,a,287,a)].
% 2.84/3.09 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(271,a,288,a)].
% 2.84/3.09 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(271,a,289,a)].
% 2.84/3.09 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(271,a,290,a)].
% 2.84/3.09 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(271,a,291,a)].
% 2.84/3.09 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(271,a,292,a)].
% 2.84/3.09 293 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 2.84/3.09 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(293,a,272,a)].
% 2.84/3.09 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(293,a,273,a)].
% 2.84/3.09 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(293,a,274,a)].
% 2.84/3.09 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(293,a,275,a)].
% 2.84/3.09 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)). [resolve(293,a,278,a)].
% 2.84/3.09 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(293,a,279,a)].
% 2.84/3.09 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_nat) = A. [resolve(293,a,280,a)].
% 2.84/3.09 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(293,a,281,a)].
% 2.84/3.09 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat))). [resolve(293,a,282,a)].
% 2.84/3.09 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat))). [resolve(293,a,283,a)].
% 2.84/3.09 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(293,a,286,a)].
% 2.84/3.09 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(293,a,287,a)].
% 2.84/3.09 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat). [resolve(293,a,288,a)].
% 2.84/3.09 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(293,a,289,a)].
% 2.84/3.09 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = B | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(293,a,290,a)].
% 2.84/3.09 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) != B | hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(293,a,291,a)].
% 2.84/3.09 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = A | -hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(293,a,292,a)].
% 2.84/3.09 294 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 2.84/3.09 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(294,a,272,a)].
% 2.84/3.09 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(294,a,273,a)].
% 2.84/3.09 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(294,a,274,a)].
% 2.84/3.09 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(294,a,275,a)].
% 2.84/3.09 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_bool),B)). [resolve(294,a,278,a)].
% 2.84/3.09 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_bool),C)). [resolve(294,a,279,a)].
% 2.84/3.09 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(294,a,280,a)].
% 2.84/3.09 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(294,a,281,a)].
% 2.84/3.09 Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool))). [resolve(294,a,282,a)].
% 2.84/3.09 Derived: hBOOL(hAPP(c_lessequals(A,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool))). [resolve(294,a,283,a)].
% 2.84/3.09 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(294,a,286,a)].
% 2.84/3.09 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(294,a,287,a)].
% 2.87/3.10 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool). [resolve(294,a,288,a)].
% 2.87/3.10 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(294,a,289,a)].
% 2.87/3.10 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -hBOOL(hAPP(c_lessequals(A,tc_bool),B)). [resolve(294,a,290,a)].
% 2.87/3.10 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | hBOOL(hAPP(c_lessequals(A,tc_bool),B)). [resolve(294,a,291,a)].
% 2.87/3.10 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -hBOOL(hAPP(c_lessequals(B,tc_bool),A)). [resolve(294,a,292,a)].
% 2.87/3.10 295 class_Lattices_Oupper__semilattice(tc_Int_Oint) # label(clsarity_Int__Oint__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 2.87/3.10 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(295,a,272,a)].
% 2.87/3.10 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(295,a,273,a)].
% 2.87/3.10 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(295,a,274,a)].
% 2.87/3.10 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(295,a,275,a)].
% 2.87/3.10 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)). [resolve(295,a,278,a)].
% 2.87/3.10 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(295,a,279,a)].
% 2.87/3.10 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_Int_Oint) = A. [resolve(295,a,280,a)].
% 2.87/3.10 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(295,a,281,a)].
% 2.87/3.10 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint))). [resolve(295,a,282,a)].
% 2.87/3.10 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_Int_Oint))). [resolve(295,a,283,a)].
% 2.87/3.10 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(295,a,286,a)].
% 2.87/3.10 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(295,a,287,a)].
% 2.87/3.10 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_Int_Oint). [resolve(295,a,288,a)].
% 2.87/3.10 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(295,a,289,a)].
% 2.87/3.10 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint) = B | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(295,a,290,a)].
% 2.87/3.10 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint) != B | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(295,a,291,a)].
% 2.87/3.10 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_Int_Oint) = A | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(295,a,292,a)].
% 2.90/3.17 296 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 2.90/3.17 297 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Ominus__class_Ominus(hAPP(c_Suc,C),D,tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_HOL_Ominus__class_Ominus(C,D,tc_nat))),B) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) # label(cls_lemma__realpow__diff_0) # label(axiom). [assumption].
% 2.90/3.17 298 -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].
% 2.90/3.17 299 -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].
% 2.90/3.17 300 -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].
% 2.90/3.17 301 -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].
% 2.90/3.17 302 -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].
% 2.90/3.17 303 -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].
% 2.90/3.17 304 -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].
% 2.90/3.17 305 -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].
% 2.90/3.17 306 -class_OrderedGroup_Omonoid__mult(A) | hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),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].
% 2.90/3.17 307 -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].
% 2.90/3.17 308 -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].
% 2.90/3.17 309 -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].
% 2.90/3.17 310 -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].
% 2.90/3.18 311 -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].
% 2.90/3.18 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Ominus__class_Ominus(hAPP(c_Suc,B),C,tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_nat),A),c_HOL_Ominus__class_Ominus(B,C,tc_nat))),A) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)). [resolve(296,a,297,a)].
% 2.90/3.18 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(296,a,298,a)].
% 2.90/3.18 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(296,a,299,a)].
% 2.90/3.18 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(296,a,300,b)].
% 2.90/3.18 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(296,a,305,a)].
% 2.90/3.18 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(296,a,306,a)].
% 2.90/3.18 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(296,a,307,a)].
% 2.90/3.18 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(296,a,308,a)].
% 2.90/3.18 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(296,a,309,a)].
% 2.90/3.18 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(296,a,311,a)].
% 2.90/3.18 312 class_OrderedGroup_Omonoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 2.90/3.18 Derived: hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_HOL_Ominus__class_Ominus(hAPP(c_Suc,B),C,tc_nat)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),A),c_HOL_Ominus__class_Ominus(B,C,tc_nat))),A) | -hBOOL(hAPP(c_lessequals(C,tc_nat),B)). [resolve(312,a,297,a)].
% 2.90/3.18 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(312,a,298,a)].
% 3.00/3.26 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(312,a,299,a)].
% 3.00/3.26 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(312,a,305,a)].
% 3.00/3.26 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(312,a,306,a)].
% 3.00/3.26 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(312,a,307,a)].
% 3.00/3.26 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(312,a,308,a)].
% 3.00/3.26 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(312,a,309,a)].
% 3.00/3.26 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(312,a,311,a)].
% 3.00/3.26 313 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 3.00/3.26 314 -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].
% 3.00/3.26 315 -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].
% 3.00/3.26 316 -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].
% 3.00/3.26 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(313,a,314,a)].
% 3.00/3.26 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(313,a,315,a)].
% 3.00/3.26 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(313,a,316,a)].
% 3.00/3.26 317 class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 3.07/3.33 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(317,a,314,a)].
% 3.07/3.33 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(317,a,315,a)].
% 3.07/3.33 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(317,a,316,a)].
% 3.07/3.33 318 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 3.07/3.33 319 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),c_SetInterval_Oord__class_OgreaterThanLessThan(B,C,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(B,C,A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_ivl__disj__un_I3_J_0) # label(axiom). [assumption].
% 3.07/3.33 320 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 3.07/3.33 321 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 3.07/3.33 322 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | C = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 3.07/3.33 323 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 3.07/3.33 324 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(B,C,A),c_SetInterval_Oord__class_OatLeastAtMost(C,D,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(B,D,A) | -hBOOL(hAPP(c_lessequals(C,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_ivl__disj__un_I21_J_0) # label(axiom). [assumption].
% 3.07/3.33 325 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(B,C,A),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(B,D,A) | -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].
% 3.07/3.33 326 -class_Orderings_Olinorder(A) | B = C | -hBOOL(hAPP(c_lessequals(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 3.07/3.33 327 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 3.07/3.33 328 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(B,C,A),c_SetInterval_Oord__class_OgreaterThanLessThan(C,D,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(B,D,A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_ivl__disj__un_I18_J_0) # label(axiom). [assumption].
% 3.07/3.33 329 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(B,C,A),c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(B,C,A) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_ivl__disj__un_I6_J_0) # label(axiom). [assumption].
% 3.07/3.33 330 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_not__leE_0) # label(axiom). [assumption].
% 3.07/3.34 331 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_lessequals(B,A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),B)) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 3.07/3.34 332 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),B)) | hBOOL(hAPP(c_lessequals(B,A),B)) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 3.07/3.34 333 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 3.07/3.34 334 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 3.07/3.34 335 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 3.07/3.34 336 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 3.07/3.34 337 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanLessThan(B,C,A),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanLessThan(B,D,A) | -hBOOL(hAPP(c_lessequals(C,A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_ivl__disj__un_I15_J_0) # label(axiom). [assumption].
% 3.07/3.34 338 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OlessThan(B,A) != c_SetInterval_Oord__class_OlessThan(C,A) | B = C # label(cls_lessThan__eq__iff_0) # label(axiom). [assumption].
% 3.07/3.34 339 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),B)) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 3.07/3.34 340 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OlessThan(B,A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OlessThan(C,A) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_ivl__disj__un_I8_J_0) # label(axiom). [assumption].
% 3.07/3.34 341 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OatLeast(B,A) != c_SetInterval_Oord__class_OatLeast(C,A) | B = C # label(cls_atLeast__eq__iff_0) # label(axiom). [assumption].
% 3.07/3.34 342 -class_Orderings_Olinorder(A) | -class_Int_Onumber(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),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].
% 3.07/3.34 343 -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(c_HOL_Oord__class_Oless(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_1) # label(axiom). [assumption].
% 3.07/3.34 344 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(B,C,A),c_SetInterval_Oord__class_OatLeast(C,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeast(B,A) | -hBOOL(hAPP(c_lessequals(B,A),C)) # label(cls_ivl__disj__un_I14_J_0) # label(axiom). [assumption].
% 3.07/3.34 345 -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].
% 3.07/3.34 346 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 3.07/3.34 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)). [resolve(318,a,319,a)].
% 3.07/3.34 Derived: A = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),A)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)). [resolve(318,a,320,a)].
% 3.07/3.34 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat),c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(A,C,tc_nat) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(318,a,324,a)].
% 3.07/3.34 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(A,C,tc_nat) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(318,a,325,a)].
% 3.07/3.34 Derived: A = B | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)). [resolve(318,a,326,a)].
% 3.07/3.34 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat),c_SetInterval_Oord__class_OgreaterThanLessThan(B,C,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(A,C,tc_nat) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(318,a,328,a)].
% 3.07/3.34 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat),c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(318,a,329,a)].
% 3.07/3.34 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(318,a,330,a)].
% 3.07/3.34 Derived: -hBOOL(hAPP(c_lessequals(A,tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),A)). [resolve(318,a,331,a)].
% 3.07/3.34 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(318,a,333,a)].
% 3.07/3.34 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanLessThan(A,C,tc_nat) | -hBOOL(hAPP(c_lessequals(B,tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)). [resolve(318,a,337,a)].
% 3.07/3.34 Derived: c_SetInterval_Oord__class_OlessThan(A,tc_nat) != c_SetInterval_Oord__class_OlessThan(B,tc_nat) | A = B. [resolve(318,a,338,a)].
% 3.07/3.34 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),A)). [resolve(318,a,339,a)].
% 3.07/3.34 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OlessThan(A,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OlessThan(B,tc_nat) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(318,a,340,a)].
% 3.07/3.34 Derived: c_SetInterval_Oord__class_OatLeast(A,tc_nat) != c_SetInterval_Oord__class_OatLeast(B,tc_nat) | A = B. [resolve(318,a,341,a)].
% 3.07/3.34 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat),c_SetInterval_Oord__class_OatLeast(B,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeast(A,tc_nat) | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(318,a,344,a)].
% 3.07/3.34 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(318,a,345,a)].
% 3.07/3.34 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),A)). [resolve(318,a,346,a)].
% 3.07/3.34 347 class_Orderings_Olinorder(tc_Int_Oint) # label(clsarity_Int__Oint__Orderings_Olinorder) # label(axiom). [assumption].
% 3.07/3.34 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_bool)),tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_Int_Oint) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)). [resolve(347,a,319,a)].
% 3.27/3.50 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(A,C,tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(347,a,324,a)].
% 3.27/3.50 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_Int_Oint),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(A,C,tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(347,a,325,a)].
% 3.27/3.50 Derived: A = B | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)). [resolve(347,a,326,a)].
% 3.27/3.50 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(B,C,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(A,C,tc_Int_Oint) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(347,a,328,a)].
% 3.27/3.50 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_Int_Oint),c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_bool)),tc_Int_Oint),tc_fun(tc_Int_Oint,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(347,a,329,a)].
% 3.27/3.50 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(347,a,330,a)].
% 3.27/3.50 Derived: -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),A)). [resolve(347,a,331,a)].
% 3.27/3.50 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(347,a,333,a)].
% 3.27/3.50 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,tc_Int_Oint),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanLessThan(A,C,tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)). [resolve(347,a,337,a)].
% 3.27/3.50 Derived: c_SetInterval_Oord__class_OlessThan(A,tc_Int_Oint) != c_SetInterval_Oord__class_OlessThan(B,tc_Int_Oint) | A = B. [resolve(347,a,338,a)].
% 3.27/3.50 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),A)). [resolve(347,a,339,a)].
% 3.27/3.50 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OlessThan(A,tc_Int_Oint),c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_bool)) = c_SetInterval_Oord__class_OlessThan(B,tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(347,a,340,a)].
% 3.27/3.50 Derived: c_SetInterval_Oord__class_OatLeast(A,tc_Int_Oint) != c_SetInterval_Oord__class_OatLeast(B,tc_Int_Oint) | A = B. [resolve(347,a,341,a)].
% 3.27/3.50 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_Int_Oint),c_SetInterval_Oord__class_OatLeast(B,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_bool)) = c_SetInterval_Oord__class_OatLeast(A,tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(347,a,344,a)].
% 3.27/3.50 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(347,a,345,a)].
% 3.27/3.50 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),A)). [resolve(347,a,346,a)].
% 3.27/3.50 348 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 3.27/3.50 349 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),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].
% 3.27/3.50 350 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__nonpos_0) # label(axiom). [assumption].
% 3.27/3.50 351 -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].
% 3.27/3.50 352 -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].
% 3.27/3.50 353 -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].
% 3.27/3.50 354 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__nonneg__pos_0) # label(axiom). [assumption].
% 3.27/3.50 355 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__pos__nonneg_0) # label(axiom). [assumption].
% 3.27/3.50 356 -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].
% 3.27/3.50 357 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__neg__neg_0) # label(axiom). [assumption].
% 3.27/3.50 358 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_add__pos__pos_0) # label(axiom). [assumption].
% 3.27/3.50 359 -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].
% 3.27/3.50 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(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(348,a,349,a)].
% 3.27/3.50 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(348,a,350,a)].
% 3.27/3.50 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(348,a,351,a)].
% 3.27/3.50 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(348,a,352,a)].
% 3.27/3.50 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(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(348,a,354,a)].
% 3.27/3.50 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(348,a,355,a)].
% 3.27/3.50 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(348,a,356,a)].
% 3.27/3.50 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(348,a,357,a)].
% 3.27/3.50 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(348,a,359,a)].
% 3.27/3.50 360 class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 3.27/3.50 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(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(360,a,349,a)].
% 3.27/3.50 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(360,a,350,a)].
% 3.27/3.50 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(360,a,351,a)].
% 3.27/3.50 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(360,a,352,a)].
% 3.31/3.58 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(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(360,a,354,a)].
% 3.31/3.58 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(360,a,355,a)].
% 3.31/3.58 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(360,a,356,a)].
% 3.31/3.58 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(360,a,357,a)].
% 3.31/3.58 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(360,a,359,a)].
% 3.31/3.58 361 class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) # label(axiom). [assumption].
% 3.31/3.58 362 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__less__zero__iff__single__less__zero_1) # label(axiom). [assumption].
% 3.31/3.58 363 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_double__add__less__zero__iff__single__less__zero_0) # label(axiom). [assumption].
% 3.31/3.58 364 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),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].
% 3.31/3.58 365 -class_OrderedGroup_Olordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_zero__less__double__add__iff__zero__less__single__add_1) # label(axiom). [assumption].
% 3.31/3.58 366 -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].
% 3.31/3.58 367 -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].
% 3.31/3.58 368 -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].
% 3.31/3.58 369 -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].
% 3.31/3.58 370 -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].
% 3.31/3.58 371 -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].
% 3.31/3.58 372 -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].
% 3.31/3.58 373 -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].
% 3.31/3.58 374 -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].
% 3.31/3.58 375 -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].
% 3.31/3.58 376 -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].
% 3.31/3.58 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A))). [resolve(361,a,364,a)].
% 3.31/3.58 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(361,a,366,a)].
% 3.31/3.58 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(361,a,367,a)].
% 3.31/3.58 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(361,a,368,a)].
% 3.31/3.58 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(361,a,369,a)].
% 3.49/3.73 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),A) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(361,a,371,a)].
% 3.49/3.73 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(361,a,373,a)].
% 3.49/3.73 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(361,a,375,a)].
% 3.49/3.73 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(361,a,376,a)].
% 3.49/3.73 377 class_OrderedGroup_Oab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 3.49/3.73 378 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat),tc_nat,A),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,E,tc_nat),tc_nat,A),A) = c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(E,D,tc_nat),tc_nat,A) | -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].
% 3.49/3.73 379 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_add__cancel__21_1) # label(axiom). [assumption].
% 3.49/3.73 380 -class_OrderedGroup_Oab__group__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) = E # label(cls_add__cancel__21_0) # label(axiom). [assumption].
% 3.49/3.73 381 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) != c_HOL_Ominus__class_Ominus(C,D,A) | C = D # label(cls_eq__eqI_0) # label(axiom). [assumption].
% 3.49/3.73 382 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,D,A) | B = C # label(cls_eq__eqI_1) # label(axiom). [assumption].
% 3.49/3.73 383 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ominus__class_Ominus(B,D,A)),c_HOL_Ominus__class_Ominus(C,E,A)) # label(cls_Deriv_Oadd__diff__add_0) # label(axiom). [assumption].
% 3.49/3.73 384 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__iff__diff__eq__0_0) # label(axiom). [assumption].
% 3.49/3.73 385 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_eq__iff__diff__eq__0_1) # label(axiom). [assumption].
% 3.49/3.73 Derived: c_HOL_Ominus__class_Ominus(c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_nat,tc_Int_Oint),c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(B,D,tc_nat),tc_nat,tc_Int_Oint),tc_Int_Oint) = c_Finite__Set_Osetsum(A,c_SetInterval_Oord__class_OatLeastLessThan(D,C,tc_nat),tc_nat,tc_Int_Oint) | -hBOOL(hAPP(c_lessequals(D,tc_nat),C)) | -hBOOL(hAPP(c_lessequals(B,tc_nat),D)). [resolve(377,a,378,a)].
% 3.49/3.73 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(377,a,380,a)].
% 3.56/3.81 Derived: c_HOL_Ominus__class_Ominus(A,A,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint) | B = C. [resolve(377,a,381,a)].
% 3.56/3.81 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,C,tc_Int_Oint) | A = B. [resolve(377,a,382,a)].
% 3.56/3.81 Derived: c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),C),D),tc_Int_Oint) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ominus__class_Ominus(A,C,tc_Int_Oint)),c_HOL_Ominus__class_Ominus(B,D,tc_Int_Oint)). [resolve(377,a,383,a)].
% 3.56/3.81 Derived: c_HOL_Ominus__class_Ominus(A,A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(377,a,384,a)].
% 3.56/3.81 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = B. [resolve(377,a,385,a)].
% 3.56/3.81 386 class_Ring__and__Field_Opordered__ring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__ring) # label(axiom). [assumption].
% 3.56/3.81 387 -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),c_HOL_Ominus__class_Ominus(E,B,A)),C)),F))) # label(cls_le__add__iff2_1) # label(axiom). [assumption].
% 3.56/3.81 388 -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),c_HOL_Ominus__class_Ominus(C,D,A)),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].
% 3.56/3.81 389 -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),c_HOL_Ominus__class_Ominus(B,E,A)),C)),D),A),F)) # label(cls_le__add__iff1_1) # label(axiom). [assumption].
% 3.56/3.81 390 -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),c_HOL_Ominus__class_Ominus(B,C,A)),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].
% 3.56/3.81 391 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ominus__class_Ominus(B,C,A)),D)),E),A),F)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(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_less__add__iff1_0) # label(axiom). [assumption].
% 3.56/3.81 392 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ominus__class_Ominus(B,E,A)),C)),D),A),F)) # label(cls_less__add__iff1_1) # label(axiom). [assumption].
% 3.56/3.81 393 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ominus__class_Ominus(C,D,A)),E)),F))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(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_less__add__iff2_0) # label(axiom). [assumption].
% 3.56/3.81 394 -class_Ring__and__Field_Opordered__ring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(D,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ominus__class_Ominus(E,B,A)),C)),F))) # label(cls_less__add__iff2_1) # label(axiom). [assumption].
% 3.56/3.81 395 -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].
% 3.56/3.81 396 -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].
% 3.56/3.81 397 -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].
% 3.56/3.81 398 -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].
% 3.56/3.81 399 -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].
% 3.56/3.81 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),c_HOL_Ominus__class_Ominus(D,A,tc_Int_Oint)),B)),E))). [resolve(386,a,387,a)].
% 3.56/3.81 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),c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint)),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(386,a,388,a)].
% 3.56/3.81 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),c_HOL_Ominus__class_Ominus(A,D,tc_Int_Oint)),B)),C),tc_Int_Oint),E)). [resolve(386,a,389,a)].
% 3.56/3.81 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),c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint)),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(386,a,390,a)].
% 3.67/3.90 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint)),C)),D),tc_Int_Oint),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),C)),D),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(386,a,391,a)].
% 3.67/3.90 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C),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_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ominus__class_Ominus(A,D,tc_Int_Oint)),B)),C),tc_Int_Oint),E)). [resolve(386,a,392,a)].
% 3.67/3.90 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint)),D)),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D)),A),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(386,a,393,a)].
% 3.67/3.90 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),C),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_HOL_Oord__class_Oless(C,tc_Int_Oint),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ominus__class_Ominus(D,A,tc_Int_Oint)),B)),E))). [resolve(386,a,394,a)].
% 3.67/3.90 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(386,a,395,a)].
% 3.67/3.90 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(386,a,396,a)].
% 3.67/3.90 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(386,a,397,a)].
% 3.67/3.90 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(386,a,398,a)].
% 3.67/3.90 400 class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 3.67/3.90 401 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),E)) # label(cls_less__eqI_1) # label(axiom). [assumption].
% 3.67/3.90 402 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(D,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_less__eqI_0) # label(axiom). [assumption].
% 3.67/3.90 403 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | hBOOL(hAPP(c_lessequals(C,A),B)) | -hBOOL(hAPP(c_lessequals(E,A),D)) # label(cls_le__eqI_1) # label(axiom). [assumption].
% 3.67/3.90 404 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | hBOOL(hAPP(c_lessequals(E,A),D)) | -hBOOL(hAPP(c_lessequals(C,A),B)) # label(cls_le__eqI_0) # label(axiom). [assumption].
% 3.67/3.90 405 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(c_HOL_Ominus__class_Ominus(B,C,A),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].
% 3.67/3.90 406 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ominus__class_Ominus(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_le__iff__diff__le__0_1) # label(axiom). [assumption].
% 3.67/3.90 407 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_less__iff__diff__less__0_0) # label(axiom). [assumption].
% 3.67/3.90 408 -class_OrderedGroup_Opordered__ab__group__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_less__iff__diff__less__0_1) # label(axiom). [assumption].
% 3.67/3.90 409 -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].
% 3.67/3.90 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,D,tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),D)). [resolve(400,a,401,a)].
% 3.67/3.90 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,D,tc_Int_Oint) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)). [resolve(400,a,402,a)].
% 3.67/3.90 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,D,tc_Int_Oint) | hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)) | -hBOOL(hAPP(c_lessequals(D,tc_Int_Oint),C)). [resolve(400,a,403,a)].
% 3.67/3.90 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,D,tc_Int_Oint) | hBOOL(hAPP(c_lessequals(D,tc_Int_Oint),C)) | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(400,a,404,a)].
% 3.67/3.90 Derived: hBOOL(hAPP(c_lessequals(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(400,a,405,a)].
% 3.67/3.90 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(400,a,406,a)].
% 3.67/3.90 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)). [resolve(400,a,407,a)].
% 3.67/3.90 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(400,a,408,a)].
% 3.67/3.90 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(400,a,409,a)].
% 3.71/3.99 410 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(17,a,26,a)].
% 3.71/3.99 411 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].
% 3.71/3.99 412 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].
% 3.71/3.99 413 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].
% 3.71/3.99 414 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].
% 3.71/3.99 415 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].
% 3.71/3.99 416 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].
% 3.71/3.99 417 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].
% 3.71/3.99 418 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].
% 3.71/3.99 419 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].
% 3.71/3.99 420 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].
% 3.71/3.99 421 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].
% 3.71/3.99 422 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].
% 3.71/3.99 423 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].
% 3.71/3.99 424 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].
% 3.71/3.99 425 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].
% 3.71/3.99 426 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].
% 3.71/3.99 427 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].
% 3.71/3.99 428 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].
% 3.71/3.99 429 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].
% 3.71/3.99 430 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].
% 3.71/3.99 431 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].
% 3.71/3.99 432 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].
% 3.71/3.99 433 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].
% 3.71/3.99 434 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].
% 3.71/3.99 435 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].
% 3.71/3.99 436 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].
% 3.71/3.99 437 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].
% 3.71/3.99 438 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].
% 3.71/3.99 439 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].
% 3.71/3.99 440 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].
% 3.71/3.99 441 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].
% 3.71/3.99 442 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].
% 3.71/3.99 443 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].
% 3.71/3.99 444 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].
% 3.71/3.99 445 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].
% 3.71/3.99 446 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].
% 3.71/3.99 447 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].
% 3.71/3.99 448 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].
% 3.71/3.99 449 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].
% 3.71/3.99 450 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].
% 3.71/3.99 451 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].
% 3.71/3.99 452 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].
% 3.71/3.99 453 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].
% 3.71/3.99 454 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].
% 3.71/3.99 455 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].
% 3.71/3.99 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(410,a,430,b)].
% 3.71/3.99 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(410,a,431,b)].
% 3.71/3.99 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(410,a,432,b)].
% 3.71/3.99 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(410,a,433,b)].
% 3.71/3.99 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(410,a,435,b)].
% 3.71/3.99 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(410,a,445,b)].
% 3.71/3.99 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(410,a,447,b)].
% 3.71/3.99 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(410,a,448,b)].
% 3.71/3.99 456 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(64,a,26,a)].
% 3.71/3.99 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(456,a,430,b)].
% 3.71/3.99 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(456,a,431,b)].
% 3.71/3.99 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(456,a,432,b)].
% 3.86/4.08 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(456,a,433,b)].
% 3.86/4.08 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(456,a,435,b)].
% 3.86/4.08 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(456,a,445,b)].
% 3.86/4.08 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(456,a,447,b)].
% 3.86/4.08 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(456,a,448,b)].
% 3.86/4.08 457 class_Ring__and__Field_Oring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oring) # label(axiom). [assumption].
% 3.86/4.08 458 -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),c_HOL_Ominus__class_Ominus(D,B,A)),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].
% 3.86/4.08 459 -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),c_HOL_Ominus__class_Ominus(B,E,A)),C)),D)) # label(cls_eq__add__iff1_1) # label(axiom). [assumption].
% 3.86/4.08 460 -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),c_HOL_Ominus__class_Ominus(B,E,A)),C)),D) = F # label(cls_eq__add__iff1_0) # label(axiom). [assumption].
% 3.86/4.08 461 -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),c_HOL_Ominus__class_Ominus(E,B,A)),C)),F) # label(cls_eq__add__iff2_0) # label(axiom). [assumption].
% 3.86/4.08 462 -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)),c_HOL_Ominus__class_Ominus(C,D,A)) = c_HOL_Ominus__class_Ominus(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),A) # label(cls_right__diff__distrib__number__of_0) # label(axiom). [assumption].
% 3.86/4.08 463 -class_Ring__and__Field_Oring(A) | -class_Int_Onumber(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ominus__class_Ominus(B,C,A)),c_Int_Onumber__class_Onumber__of(D,A)) = c_HOL_Ominus__class_Ominus(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)),A) # label(cls_left__diff__distrib__number__of_0) # label(axiom). [assumption].
% 3.86/4.08 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_HOL_Ominus__class_Ominus(C,A,tc_Int_Oint)),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(457,a,458,a)].
% 3.97/4.23 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),c_HOL_Ominus__class_Ominus(A,D,tc_Int_Oint)),B)),C)). [resolve(457,a,459,a)].
% 3.97/4.23 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),c_HOL_Ominus__class_Ominus(A,D,tc_Int_Oint)),B)),C) = E. [resolve(457,a,460,a)].
% 3.97/4.23 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),c_HOL_Ominus__class_Ominus(D,A,tc_Int_Oint)),B)),E). [resolve(457,a,461,a)].
% 3.97/4.23 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)),c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint)) = c_HOL_Ominus__class_Ominus(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),tc_Int_Oint). [resolve(457,a,462,a)].
% 3.97/4.23 Derived: -class_Int_Onumber(tc_Int_Oint) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(C,tc_Int_Oint)) = c_HOL_Ominus__class_Ominus(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)),tc_Int_Oint). [resolve(457,a,463,a)].
% 3.97/4.23 464 class_OrderedGroup_Ogroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 3.97/4.23 465 -class_OrderedGroup_Ogroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ominus__class_Ominus(B,C,A)),C) = B # label(cls_diff__add__cancel_0) # label(axiom). [assumption].
% 3.97/4.23 466 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),C,A) = B # label(cls_add__diff__cancel_0) # label(axiom). [assumption].
% 3.97/4.23 467 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus__eq_1) # label(axiom). [assumption].
% 3.97/4.23 468 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_diff__0__right_0) # label(axiom). [assumption].
% 3.97/4.23 469 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_diff__self_0) # label(axiom). [assumption].
% 3.97/4.23 470 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_right__minus__eq_0) # label(axiom). [assumption].
% 3.97/4.23 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint)),B) = A. [resolve(464,a,465,a)].
% 3.97/4.23 Derived: c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B),B,tc_Int_Oint) = A. [resolve(464,a,466,a)].
% 3.97/4.23 Derived: c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = A. [resolve(464,a,468,a)].
% 3.97/4.23 471 class_OrderedGroup_Olordered__ab__group__add__join(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__join) # label(axiom). [assumption].
% 4.15/4.45 472 -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].
% 4.15/4.45 473 -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].
% 4.15/4.45 474 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 4.15/4.45 475 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 4.15/4.45 476 class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 4.15/4.45 477 class_Divides_Oring__div(tc_Int_Oint) # label(clsarity_Int__Oint__Divides_Oring__div) # label(axiom). [assumption].
% 4.15/4.45 478 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(B,D,A),c_Divides_Odiv__class_Omod(C,D,A),A),D,A) # label(cls_mod__diff__eq_0) # label(axiom). [assumption].
% 4.15/4.45 479 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(B,D,A),C,A),D,A) # label(cls_mod__diff__left__eq_0) # label(axiom). [assumption].
% 4.15/4.45 480 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(B,c_Divides_Odiv__class_Omod(C,D,A),A),D,A) # label(cls_mod__diff__right__eq_0) # label(axiom). [assumption].
% 4.15/4.45 481 -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(c_HOL_Ominus__class_Ominus(E,B,A),C,A) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(F,D,A),C,A) # label(cls_mod__diff__cong_0) # label(axiom). [assumption].
% 4.15/4.45 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint). [resolve(477,a,478,a)].
% 4.15/4.45 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint),B,tc_Int_Oint),C,tc_Int_Oint). [resolve(477,a,479,a)].
% 4.15/4.45 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint). [resolve(477,a,480,a)].
% 4.15/4.45 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(C,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(D,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(E,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(D,A,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(E,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(477,a,481,a)].
% 4.15/4.45 482 class_Ring__and__Field_Oidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 4.15/4.45 483 -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].
% 4.15/4.45 484 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Osubr0__iff_1) # label(axiom). [assumption].
% 4.15/4.45 485 -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].
% 4.15/4.45 486 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_class__ringb_Osubr0__iff_0) # label(axiom). [assumption].
% 4.15/4.45 487 -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].
% 4.15/4.45 488 -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].
% 4.15/4.45 489 -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].
% 4.15/4.45 490 -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].
% 4.15/4.45 491 -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].
% 4.15/4.45 492 -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].
% 4.15/4.45 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),C) | B = C. [resolve(482,a,483,a)].
% 4.15/4.45 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | A != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),B) | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(482,a,485,a)].
% 4.15/4.45 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | A = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),c_HOL_Ozero__class_Ozero(tc_Int_Oint)). [resolve(482,a,487,a)].
% 4.15/4.45 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),D)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),C),B)) | B = D | A = C. [resolve(482,a,488,a)].
% 4.15/4.45 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),C)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Int_Oint),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),D)) | C = D | B = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(482,a,492,a)].
% 4.63/4.86 493 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 4.63/4.86 494 -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].
% 4.63/4.86 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(493,a,494,a)].
% 4.63/4.86 495 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 4.63/4.86 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(495,a,494,a)].
% 4.63/4.86 496 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 4.63/4.86 497 -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].
% 4.63/4.86 498 -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].
% 4.63/4.86 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(496,a,498,a)].
% 4.63/4.86 499 class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 4.63/4.86 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(499,a,498,a)].
% 4.63/4.86 500 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 4.63/4.86 501 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__strict__mono_0) # label(axiom). [assumption].
% 4.63/4.86 502 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 4.63/4.86 503 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 4.63/4.86 504 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_add__strict__left__mono_0) # label(axiom). [assumption].
% 4.63/4.86 505 -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__strict__right__mono_0) # label(axiom). [assumption].
% 4.63/4.86 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(500,a,501,a)].
% 4.70/4.93 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(500,a,502,a)].
% 4.70/4.93 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(500,a,503,a)].
% 4.70/4.93 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(500,a,504,a)].
% 4.70/4.93 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(500,a,505,a)].
% 4.70/4.93 506 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 4.70/4.93 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(506,a,501,a)].
% 4.70/4.93 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(506,a,502,a)].
% 4.70/4.93 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(506,a,503,a)].
% 4.70/4.93 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(B,tc_Int_Oint),C)). [resolve(506,a,504,a)].
% 4.70/4.93 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(506,a,505,a)].
% 4.70/4.93 507 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 4.70/4.93 508 -class_Ring__and__Field_Osemiring__1(A) | c_Int_Oiszero(c_HOL_Ozero__class_Ozero(A),A) # label(cls_iszero__0_0) # label(axiom). [assumption].
% 4.70/4.93 509 -class_Ring__and__Field_Osemiring__1(A) | B = c_HOL_Ozero__class_Ozero(A) | -c_Int_Oiszero(B,A) # label(cls_iszero__def_0) # label(axiom). [assumption].
% 4.70/4.93 510 -class_Ring__and__Field_Osemiring__1(A) | -c_Int_Oiszero(c_HOL_Oone__class_Oone(A),A) # label(cls_not__iszero__1_0) # label(axiom). [assumption].
% 4.70/4.93 511 -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].
% 4.70/4.93 512 -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].
% 4.70/4.93 Derived: c_Int_Oiszero(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). [resolve(507,a,508,a)].
% 4.70/4.93 Derived: A = c_HOL_Ozero__class_Ozero(tc_nat) | -c_Int_Oiszero(A,tc_nat). [resolve(507,a,509,a)].
% 4.70/4.93 Derived: -c_Int_Oiszero(c_HOL_Oone__class_Oone(tc_nat),tc_nat). [resolve(507,a,510,a)].
% 5.00/5.26 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(507,a,512,a)].
% 5.00/5.26 513 class_Ring__and__Field_Osemiring__1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 5.00/5.26 Derived: c_Int_Oiszero(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(513,a,508,a)].
% 5.00/5.26 Derived: A = c_HOL_Ozero__class_Ozero(tc_Int_Oint) | -c_Int_Oiszero(A,tc_Int_Oint). [resolve(513,a,509,a)].
% 5.00/5.26 Derived: -c_Int_Oiszero(c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint). [resolve(513,a,510,a)].
% 5.00/5.26 514 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].
% 5.00/5.26 515 -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].
% 5.00/5.26 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(514,a,515,a)].
% 5.00/5.26 516 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 5.00/5.26 517 -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].
% 5.00/5.26 518 -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].
% 5.00/5.26 519 class_OrderedGroup_Omonoid__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 5.00/5.26 520 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 5.00/5.26 521 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__less__le__imp__less_0) # label(axiom). [assumption].
% 5.00/5.26 522 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_lessequals(B,A),D)) # label(cls_mult__le__less__imp__less_0) # label(axiom). [assumption].
% 5.00/5.26 523 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__strict__mono_H_0) # label(axiom). [assumption].
% 5.00/5.26 524 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))) # label(cls_mult__less__imp__less__right_0) # label(axiom). [assumption].
% 5.00/5.26 525 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) # label(cls_mult__less__imp__less__left_0) # label(axiom). [assumption].
% 5.00/5.26 526 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__strict__mono_0) # label(axiom). [assumption].
% 5.00/5.26 527 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),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].
% 5.00/5.26 528 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_lessequals(B,A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),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].
% 5.00/5.26 529 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_mult__strict__left__mono_0) # label(axiom). [assumption].
% 5.00/5.26 530 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__strict__right__mono_0) # label(axiom). [assumption].
% 5.00/5.26 531 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__pos__pos_0) # label(axiom). [assumption].
% 5.00/5.26 532 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B))) # label(cls_zero__less__mult__pos_0) # label(axiom). [assumption].
% 5.00/5.26 533 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) # label(cls_zero__less__mult__pos2_0) # label(axiom). [assumption].
% 5.00/5.26 534 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__neg__pos_0) # label(axiom). [assumption].
% 5.00/5.26 535 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) # label(cls_mult__pos__neg_0) # label(axiom). [assumption].
% 5.00/5.26 536 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),C)) # label(cls_mult__pos__neg2_0) # label(axiom). [assumption].
% 5.00/5.26 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(520,a,521,a)].
% 5.00/5.26 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_lessequals(A,tc_nat),C)). [resolve(520,a,522,a)].
% 5.00/5.26 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(520,a,523,a)].
% 5.00/5.26 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(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(520,a,524,a)].
% 5.00/5.26 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(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(520,a,525,a)].
% 5.00/5.26 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(520,a,526,a)].
% 5.00/5.26 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),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(520,a,527,a)].
% 5.00/5.26 Derived: hBOOL(hAPP(c_lessequals(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),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(520,a,528,a)].
% 5.00/5.26 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(520,a,529,a)].
% 5.00/5.26 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(520,a,530,a)].
% 5.00/5.26 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(520,a,531,a)].
% 5.00/5.26 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A))). [resolve(520,a,532,a)].
% 5.00/5.26 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))). [resolve(520,a,533,a)].
% 5.00/5.26 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(520,a,534,a)].
% 5.00/5.26 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(520,a,535,a)].
% 5.00/5.26 537 class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 5.00/5.26 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(537,a,521,a)].
% 5.00/5.26 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),C)). [resolve(537,a,522,a)].
% 5.00/5.26 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(537,a,523,a)].
% 5.00/5.26 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(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(537,a,524,a)].
% 5.00/5.26 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(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(537,a,525,a)].
% 5.00/5.26 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(537,a,526,a)].
% 5.04/5.33 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),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(537,a,527,a)].
% 5.04/5.33 Derived: hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),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(537,a,528,a)].
% 5.04/5.33 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),C)). [resolve(537,a,529,a)].
% 5.04/5.33 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(537,a,530,a)].
% 5.04/5.33 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(537,a,531,a)].
% 5.04/5.33 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),B),A))). [resolve(537,a,532,a)].
% 5.04/5.33 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_Int_Oint),A),B))). [resolve(537,a,533,a)].
% 5.04/5.33 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))). [resolve(537,a,534,a)].
% 5.04/5.33 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint),A)). [resolve(537,a,535,a)].
% 5.04/5.33 538 class_Ring__and__Field_Oordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 5.04/5.33 539 -class_Ring__and__Field_Oordered__semiring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(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__less__imp__less_0) # label(axiom). [assumption].
% 5.04/5.33 540 -class_Ring__and__Field_Oordered__semiring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(c_lessequals(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(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__less__imp__less_0) # label(axiom). [assumption].
% 5.28/5.53 541 class_Ring__and__Field_Oordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 5.28/5.53 542 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 5.28/5.53 543 -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].
% 5.28/5.53 544 class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 5.28/5.53 545 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 5.28/5.53 546 -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].
% 5.28/5.53 547 -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].
% 5.28/5.53 548 class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 5.28/5.53 549 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 5.28/5.53 550 -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].
% 5.28/5.53 551 -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].
% 5.28/5.53 552 -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].
% 5.28/5.53 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(549,a,550,a)].
% 5.28/5.53 553 class_Ring__and__Field_Osemiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 5.28/5.53 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(553,a,550,a)].
% 5.53/5.78 554 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 5.53/5.78 555 -class_Ring__and__Field_Oordered__comm__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_mult__strict__left__mono__comm_0) # label(axiom). [assumption].
% 5.53/5.78 556 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].
% 5.53/5.78 557 class_Ring__and__Field_Omult__mono1(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 5.53/5.78 558 -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].
% 5.53/5.78 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(557,a,558,a)].
% 5.53/5.78 559 class_Ring__and__Field_Omult__mono1(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 5.53/5.78 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(559,a,558,a)].
% 5.53/5.78 560 class_Ring__and__Field_Omult__mono(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 5.53/5.78 561 -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].
% 5.53/5.78 562 -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].
% 5.53/5.78 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(560,a,562,a)].
% 5.53/5.78 563 class_Ring__and__Field_Omult__mono(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 5.53/5.78 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(563,a,562,a)].
% 5.53/5.78 564 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 5.53/5.78 565 -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].
% 5.53/5.78 566 -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].
% 5.58/5.84 567 -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].
% 5.58/5.84 568 -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].
% 5.58/5.84 569 -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].
% 5.58/5.84 570 -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].
% 5.58/5.84 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(564,a,565,a)].
% 5.58/5.84 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(564,a,566,a)].
% 5.58/5.84 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(564,a,567,a)].
% 5.58/5.84 571 class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 5.58/5.84 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(571,a,566,a)].
% 5.58/5.84 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(571,a,567,a)].
% 5.58/5.84 572 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 5.58/5.84 573 -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].
% 5.58/5.84 574 -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].
% 5.74/5.98 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(572,a,573,a)].
% 5.74/5.98 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(572,a,574,a)].
% 5.74/5.98 575 class_Ring__and__Field_Opordered__semiring(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 5.74/5.98 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(575,a,573,a)].
% 5.74/5.98 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(575,a,574,a)].
% 5.74/5.98 576 class_Int_Oring__char__0(tc_Int_Oint) # label(clsarity_Int__Oint__Int_Oring__char__0) # label(axiom). [assumption].
% 5.74/5.98 577 -class_Int_Oring__char__0(A) | -class_Int_Onumber__ring(A) | -c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(B),A),A) # label(cls_iszero__number__of__Bit1_0) # label(axiom). [assumption].
% 5.74/5.98 578 -class_Int_Oring__char__0(A) | -class_Int_Onumber__ring(A) | c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(B),A),A) | -c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(B,A),A) # label(cls_iszero__number__of__Bit0_1) # label(axiom). [assumption].
% 5.74/5.98 579 -class_Int_Oring__char__0(A) | -class_Int_Onumber__ring(A) | c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(B,A),A) | -c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(B),A),A) # label(cls_iszero__number__of__Bit0_0) # label(axiom). [assumption].
% 5.74/5.98 580 -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].
% 5.74/5.98 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | -c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(A),tc_Int_Oint),tc_Int_Oint). [resolve(576,a,577,a)].
% 5.74/5.98 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(A),tc_Int_Oint),tc_Int_Oint) | -c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint). [resolve(576,a,578,a)].
% 5.74/5.98 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint),tc_Int_Oint) | -c_Int_Oiszero(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(A),tc_Int_Oint),tc_Int_Oint). [resolve(576,a,579,a)].
% 5.74/5.98 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint) | A = B. [resolve(576,a,580,a)].
% 5.74/5.98 581 class_OrderedGroup_Olordered__ab__group__add__meet(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__meet) # label(axiom). [assumption].
% 5.79/6.04 582 -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].
% 5.79/6.04 583 -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].
% 5.79/6.04 584 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 5.79/6.04 585 -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].
% 5.79/6.04 586 -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].
% 5.79/6.04 587 -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].
% 5.79/6.04 588 -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].
% 5.79/6.04 589 -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].
% 5.79/6.04 590 -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].
% 5.79/6.04 591 -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].
% 5.79/6.04 592 -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].
% 5.79/6.04 593 -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].
% 5.79/6.04 594 -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].
% 5.79/6.04 595 -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].
% 5.79/6.04 596 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),D)) # label(cls_less__infI2_0) # label(axiom). [assumption].
% 5.79/6.04 597 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_less__infI1_0) # label(axiom). [assumption].
% 5.79/6.04 598 -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].
% 5.82/6.05 599 -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].
% 5.82/6.05 600 -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].
% 5.82/6.05 601 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 5.82/6.05 602 -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].
% 5.82/6.05 603 -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].
% 5.82/6.05 604 -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].
% 5.82/6.05 605 -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].
% 5.82/6.05 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(584,a,585,a)].
% 5.82/6.05 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(584,a,586,a)].
% 5.82/6.05 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(584,a,587,a)].
% 5.82/6.05 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(584,a,588,a)].
% 5.82/6.05 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(584,a,591,a)].
% 5.82/6.05 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(584,a,594,a)].
% 5.82/6.05 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(584,a,595,a)].
% 5.82/6.05 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,tc_fun(D,A)),E)). [resolve(584,a,596,a)].
% 5.82/6.05 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_fun(D,A)),E)). [resolve(584,a,597,a)].
% 5.82/6.05 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(584,a,598,a)].
% 5.82/6.05 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(584,a,599,a)].
% 5.82/6.05 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(584,a,600,a)].
% 5.82/6.05 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(584,a,601,a)].
% 5.82/6.05 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(584,a,602,a)].
% 5.82/6.05 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(584,a,603,a)].
% 5.82/6.05 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(584,a,604,a)].
% 5.82/6.05 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(584,a,605,a)].
% 5.82/6.05 606 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 5.82/6.05 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(606,a,585,a)].
% 5.82/6.05 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(606,a,586,a)].
% 5.82/6.05 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(606,a,587,a)].
% 5.82/6.05 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(606,a,588,a)].
% 5.82/6.05 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(606,a,591,a)].
% 5.82/6.05 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat),B)). [resolve(606,a,594,a)].
% 5.82/6.05 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat),A)). [resolve(606,a,595,a)].
% 5.82/6.05 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)). [resolve(606,a,596,a)].
% 5.82/6.05 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(606,a,597,a)].
% 5.82/6.05 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = B | -hBOOL(hAPP(c_lessequals(B,tc_nat),A)). [resolve(606,a,598,a)].
% 5.82/6.05 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) != A | hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(606,a,599,a)].
% 5.82/6.05 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = A | -hBOOL(hAPP(c_lessequals(A,tc_nat),B)). [resolve(606,a,600,a)].
% 5.82/6.05 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_nat) = A. [resolve(606,a,601,a)].
% 5.82/6.05 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(606,a,602,a)].
% 5.82/6.05 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(606,a,603,a)].
% 5.82/6.05 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(606,a,604,a)].
% 5.82/6.05 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_nat). [resolve(606,a,605,a)].
% 5.82/6.05 607 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 5.82/6.05 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(607,a,585,a)].
% 5.82/6.05 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(607,a,586,a)].
% 5.82/6.05 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(607,a,587,a)].
% 5.82/6.05 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(607,a,588,a)].
% 5.82/6.05 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(607,a,591,a)].
% 5.82/6.05 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool),B)). [resolve(607,a,594,a)].
% 5.82/6.05 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool),A)). [resolve(607,a,595,a)].
% 5.82/6.05 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_bool),C)). [resolve(607,a,596,a)].
% 5.82/6.05 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_bool),C)). [resolve(607,a,597,a)].
% 5.82/6.05 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -hBOOL(hAPP(c_lessequals(B,tc_bool),A)). [resolve(607,a,598,a)].
% 5.82/6.05 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | hBOOL(hAPP(c_lessequals(A,tc_bool),B)). [resolve(607,a,599,a)].
% 5.82/6.05 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -hBOOL(hAPP(c_lessequals(A,tc_bool),B)). [resolve(607,a,600,a)].
% 5.82/6.05 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(607,a,601,a)].
% 5.82/6.05 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(607,a,602,a)].
% 5.82/6.05 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(607,a,603,a)].
% 5.82/6.05 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(607,a,604,a)].
% 5.82/6.05 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(607,a,605,a)].
% 5.82/6.06 608 class_Lattices_Olower__semilattice(tc_Int_Oint) # label(clsarity_Int__Oint__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 5.82/6.06 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(608,a,585,a)].
% 5.82/6.06 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(608,a,586,a)].
% 5.82/6.06 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(608,a,587,a)].
% 5.82/6.06 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(608,a,588,a)].
% 5.82/6.06 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(608,a,591,a)].
% 6.12/6.40 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),tc_Int_Oint),B)). [resolve(608,a,594,a)].
% 6.12/6.40 Derived: hBOOL(hAPP(c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),tc_Int_Oint),A)). [resolve(608,a,595,a)].
% 6.12/6.40 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_Int_Oint),C)). [resolve(608,a,596,a)].
% 6.12/6.40 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),tc_Int_Oint),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_Int_Oint),C)). [resolve(608,a,597,a)].
% 6.12/6.40 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint) = B | -hBOOL(hAPP(c_lessequals(B,tc_Int_Oint),A)). [resolve(608,a,598,a)].
% 6.12/6.40 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint) != A | hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(608,a,599,a)].
% 6.12/6.40 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint) = A | -hBOOL(hAPP(c_lessequals(A,tc_Int_Oint),B)). [resolve(608,a,600,a)].
% 6.12/6.40 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_Int_Oint) = A. [resolve(608,a,601,a)].
% 6.12/6.40 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(608,a,602,a)].
% 6.12/6.40 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(608,a,603,a)].
% 6.12/6.40 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(608,a,604,a)].
% 6.12/6.40 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_Int_Oint). [resolve(608,a,605,a)].
% 6.12/6.40 609 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].
% 6.12/6.40 610 -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].
% 6.12/6.40 611 -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].
% 6.12/6.40 612 -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].
% 6.12/6.40 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(609,a,612,a)].
% 6.12/6.40 613 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 6.12/6.40 614 -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].
% 6.12/6.40 615 class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 6.12/6.40 616 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 6.12/6.40 617 c_fequal(A,A,B) # laCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------