TSTP Solution File: LCL747-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL747-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 : Sun Jul 17 13:49:46 EDT 2022
% Result : Timeout 300.09s 300.42s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL747-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 3 04:43:30 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.04/1.38 ============================== Prover9 ===============================
% 1.04/1.38 Prover9 (32) version 2009-11A, November 2009.
% 1.04/1.38 Process 14558 was started by sandbox on n021.cluster.edu,
% 1.04/1.38 Sun Jul 3 04:43:31 2022
% 1.04/1.38 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_14252_n021.cluster.edu".
% 1.04/1.38 ============================== end of head ===========================
% 1.04/1.38
% 1.04/1.38 ============================== INPUT =================================
% 1.04/1.38
% 1.04/1.38 % Reading from file /tmp/Prover9_14252_n021.cluster.edu
% 1.04/1.38
% 1.04/1.38 set(prolog_style_variables).
% 1.04/1.38 set(auto2).
% 1.04/1.38 % set(auto2) -> set(auto).
% 1.04/1.38 % set(auto) -> set(auto_inference).
% 1.04/1.38 % set(auto) -> set(auto_setup).
% 1.04/1.38 % set(auto_setup) -> set(predicate_elim).
% 1.04/1.38 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.04/1.38 % set(auto) -> set(auto_limits).
% 1.04/1.38 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.04/1.38 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.04/1.38 % set(auto) -> set(auto_denials).
% 1.04/1.38 % set(auto) -> set(auto_process).
% 1.04/1.38 % set(auto2) -> assign(new_constants, 1).
% 1.04/1.38 % set(auto2) -> assign(fold_denial_max, 3).
% 1.04/1.38 % set(auto2) -> assign(max_weight, "200.000").
% 1.04/1.38 % set(auto2) -> assign(max_hours, 1).
% 1.04/1.38 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.04/1.38 % set(auto2) -> assign(max_seconds, 0).
% 1.04/1.38 % set(auto2) -> assign(max_minutes, 5).
% 1.04/1.38 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.04/1.38 % set(auto2) -> set(sort_initial_sos).
% 1.04/1.38 % set(auto2) -> assign(sos_limit, -1).
% 1.04/1.38 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.04/1.38 % set(auto2) -> assign(max_megs, 400).
% 1.04/1.38 % set(auto2) -> assign(stats, some).
% 1.04/1.38 % set(auto2) -> clear(echo_input).
% 1.04/1.38 % set(auto2) -> set(quiet).
% 1.04/1.38 % set(auto2) -> clear(print_initial_clauses).
% 1.04/1.38 % set(auto2) -> clear(print_given).
% 1.04/1.38 assign(lrs_ticks,-1).
% 1.04/1.38 assign(sos_limit,10000).
% 1.04/1.38 assign(order,kbo).
% 1.04/1.38 set(lex_order_vars).
% 1.04/1.38 clear(print_given).
% 1.04/1.38
% 1.04/1.38 % formulas(sos). % not echoed (728 formulas)
% 1.04/1.38
% 1.04/1.38 ============================== end of input ==========================
% 1.04/1.38
% 1.04/1.38 % From the command line: assign(max_seconds, 300).
% 1.04/1.38
% 1.04/1.38 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.04/1.38
% 1.04/1.38 % Formulas that are not ordinary clauses:
% 1.04/1.38
% 1.04/1.38 ============================== end of process non-clausal formulas ===
% 1.04/1.38
% 1.04/1.38 ============================== PROCESS INITIAL CLAUSES ===============
% 1.04/1.38
% 1.04/1.38 ============================== PREDICATE ELIMINATION =================
% 1.04/1.38 1 class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) # label(axiom). [assumption].
% 1.04/1.38 2 -class_OrderedGroup_Opordered__comm__monoid__add(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(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].
% 1.04/1.38 3 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_add__nonneg__nonneg_0) # label(axiom). [assumption].
% 1.04/1.38 4 -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].
% 1.04/1.38 5 -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(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_1) # label(axiom). [assumption].
% 1.04/1.38 6 -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(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_add__nonneg__eq__0__iff_0) # label(axiom). [assumption].
% 1.04/1.38 7 -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(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_add__nonneg__pos_0) # label(axiom). [assumption].
% 1.04/1.38 8 -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(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(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].
% 1.04/1.38 9 -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(hAPP(c_lessequals(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__nonpos__neg_0) # label(axiom). [assumption].
% 1.04/1.38 10 -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(hAPP(c_lessequals(A),C),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].
% 1.04/1.38 11 -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].
% 1.04/1.38 12 -class_OrderedGroup_Opordered__comm__monoid__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_add__nonpos__nonpos_0) # label(axiom). [assumption].
% 1.04/1.38 Derived: -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,2,a)].
% 1.04/1.38 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(1,a,3,a)].
% 1.04/1.38 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(1,a,4,a)].
% 1.04/1.38 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | B = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,5,a)].
% 1.04/1.38 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,6,a)].
% 1.04/1.41 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(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(1,a,7,a)].
% 1.04/1.41 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(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(1,a,8,a)].
% 1.04/1.41 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(hAPP(c_lessequals(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(1,a,9,a)].
% 1.04/1.41 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(hAPP(c_lessequals(tc_nat),B),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(1,a,10,a)].
% 1.04/1.41 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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(1,a,11,a)].
% 1.04/1.41 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(1,a,12,a)].
% 1.04/1.41 13 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.04/1.41 14 -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].
% 1.04/1.41 15 -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].
% 1.04/1.41 16 -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].
% 1.04/1.41 17 -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].
% 1.04/1.41 18 -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].
% 1.04/1.41 19 -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].
% 1.04/1.41 20 -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].
% 1.04/1.41 21 -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].
% 1.04/1.41 22 -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].
% 1.04/1.41 23 -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].
% 1.04/1.41 24 -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].
% 1.04/1.41 25 -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].
% 1.04/1.41 26 -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].
% 1.04/1.41 27 -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].
% 1.04/1.41 28 -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].
% 1.04/1.41 29 -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].
% 1.04/1.41 30 -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].
% 1.04/1.41 31 -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].
% 1.04/1.41 32 -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].
% 1.04/1.41 33 -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].
% 1.04/1.41 34 -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].
% 1.04/1.41 35 -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].
% 1.04/1.41 36 -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].
% 1.04/1.41 37 -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].
% 1.04/1.41 38 -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].
% 1.04/1.41 39 -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].
% 1.04/1.41 40 -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].
% 1.04/1.41 41 -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].
% 1.04/1.41 42 -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].
% 1.04/1.41 43 -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].
% 1.04/1.41 44 -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].
% 1.04/1.41 45 -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].
% 1.04/1.41 46 -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].
% 1.04/1.41 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(13,a,14,a)].
% 1.04/1.41 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(13,a,15,a)].
% 1.04/1.41 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(13,a,17,a)].
% 1.04/1.41 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(13,a,18,a)].
% 1.04/1.41 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(13,a,19,a)].
% 1.04/1.41 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A) = A. [resolve(13,a,21,a)].
% 1.04/1.41 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)) = A. [resolve(13,a,22,a)].
% 1.04/1.41 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(13,a,24,a)].
% 1.04/1.41 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(13,a,26,a)].
% 1.04/1.41 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(13,a,27,a)].
% 1.04/1.41 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(13,a,28,a)].
% 1.04/1.41 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(13,a,29,a)].
% 1.04/1.41 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(13,a,30,a)].
% 1.04/1.41 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(13,a,32,a)].
% 1.04/1.41 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))). [resolve(13,a,33,a)].
% 1.04/1.41 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),D)). [resolve(13,a,34,a)].
% 1.04/1.41 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(13,a,35,a)].
% 1.04/1.41 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(13,a,36,a)].
% 1.04/1.41 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(13,a,38,a)].
% 1.04/1.41 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(13,a,39,a)].
% 1.04/1.41 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(13,a,40,a)].
% 1.04/1.41 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(13,a,41,a)].
% 1.04/1.45 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(13,a,42,a)].
% 1.04/1.45 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(13,a,43,a)].
% 1.04/1.45 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(13,a,45,a)].
% 1.04/1.45 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(13,a,46,a)].
% 1.04/1.45 47 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.04/1.45 48 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_comm__monoid__add_Omult__assoc_0) # label(axiom). [assumption].
% 1.04/1.45 49 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_comm__monoid__add_Omult__left__commute_0) # label(axiom). [assumption].
% 1.04/1.45 50 -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(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) # label(cls_add__strict__increasing2_0) # label(axiom). [assumption].
% 1.04/1.45 51 -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(hAPP(c_lessequals(A),B),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].
% 1.04/1.45 52 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) # label(cls_add__increasing_0) # label(axiom). [assumption].
% 1.04/1.45 53 -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A) | -class_OrderedGroup_Ocomm__monoid__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),D)) # label(cls_add__increasing2_0) # label(axiom). [assumption].
% 1.04/1.45 54 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_comm__monoid__add_Omult__commute_0) # label(axiom). [assumption].
% 1.04/1.45 55 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_comm__monoid__add_Omult__1_0) # label(axiom). [assumption].
% 1.04/1.45 56 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_comm__monoid__add_Omult__1__right_0) # label(axiom). [assumption].
% 1.04/1.45 57 -class_OrderedGroup_Ocomm__monoid__add(A) | c_List_Olistsum(c_List_Omap(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Oplus__class_Oplus(A)),C),B,A,A),D),E,B,A),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_List_Olistsum(c_List_Omap(C,E,B,A),A)),c_List_Olistsum(c_List_Omap(D,E,B,A),A)) # label(cls_listsum__addf_0) # label(axiom). [assumption].
% 1.04/1.52 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(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)). [resolve(47,a,50,b)].
% 1.04/1.52 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(hAPP(c_lessequals(tc_nat),A),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)). [resolve(47,a,51,b)].
% 1.04/1.52 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)). [resolve(47,a,52,b)].
% 1.04/1.52 Derived: -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)). [resolve(47,a,53,b)].
% 1.04/1.52 Derived: c_List_Olistsum(c_List_Omap(hAPP(c_COMBS(hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),A),c_HOL_Oplus__class_Oplus(tc_nat)),B),A,tc_nat,tc_nat),C),D,A,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_List_Olistsum(c_List_Omap(B,D,A,tc_nat),tc_nat)),c_List_Olistsum(c_List_Omap(C,D,A,tc_nat),tc_nat)). [resolve(47,a,57,a)].
% 1.04/1.52 58 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 1.04/1.52 59 -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].
% 1.04/1.52 60 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 1.04/1.52 61 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_of__nat__1_0) # label(axiom). [assumption].
% 1.04/1.52 62 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A)) # label(cls_of__nat__Suc_0) # label(axiom). [assumption].
% 1.04/1.52 63 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_of__nat__0_0) # label(axiom). [assumption].
% 1.04/1.52 64 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)) # label(cls_of__nat__add_0) # label(axiom). [assumption].
% 1.04/1.52 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(60,a,61,a)].
% 1.04/1.52 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_Suc(A),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)). [resolve(60,a,62,a)].
% 1.04/1.52 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(60,a,63,a)].
% 1.04/1.52 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat)). [resolve(60,a,64,a)].
% 1.04/1.56 65 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 1.04/1.56 66 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Ozero__class_Ozero(A) != c_HOL_Oone__class_Oone(A) # label(cls_zero__neq__one_0) # label(axiom). [assumption].
% 1.04/1.56 67 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Oone__class_Oone(A) != c_HOL_Ozero__class_Ozero(A) # label(cls_one__neq__zero_0) # label(axiom). [assumption].
% 1.04/1.56 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(65,a,66,a)].
% 1.04/1.56 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(65,a,67,a)].
% 1.04/1.56 68 class_Ring__and__Field_Oordered__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring__strict) # label(axiom). [assumption].
% 1.04/1.56 69 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) # label(cls_mult__left__le__imp__le_0) # label(axiom). [assumption].
% 1.04/1.56 70 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D))) # label(cls_mult__right__le__imp__le_0) # label(axiom). [assumption].
% 1.04/1.56 71 -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(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(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].
% 1.04/1.56 72 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(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].
% 1.04/1.56 73 -class_Ring__and__Field_Oordered__semiring__strict(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(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].
% 1.04/1.56 74 -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].
% 1.04/1.56 75 -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].
% 1.04/1.56 76 -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].
% 1.04/1.56 77 -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].
% 1.04/1.56 78 -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].
% 1.04/1.56 79 -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(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_mult__less__le__imp__less_0) # label(axiom). [assumption].
% 1.04/1.56 80 -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(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(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(hAPP(c_lessequals(A),B),D)) # label(cls_mult__le__less__imp__less_0) # label(axiom). [assumption].
% 1.04/1.56 81 -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].
% 1.04/1.56 82 -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].
% 1.04/1.56 83 -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].
% 1.04/1.56 84 -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(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(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].
% 1.04/1.56 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))). [resolve(68,a,69,a)].
% 1.04/1.56 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),C)) | -hBOOL(hAPP(hAPP(c_lessequals(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(68,a,70,a)].
% 1.04/1.56 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(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(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(68,a,71,a)].
% 1.04/1.56 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(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(68,a,72,a)].
% 1.04/1.56 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(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(68,a,73,a)].
% 1.04/1.56 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(68,a,74,a)].
% 1.04/1.56 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(68,a,75,a)].
% 1.04/1.56 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(68,a,76,a)].
% 1.04/1.56 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(68,a,77,a)].
% 1.04/1.56 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(68,a,78,a)].
% 1.04/1.56 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(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(68,a,79,a)].
% 1.04/1.56 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(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(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(hAPP(c_lessequals(tc_nat),A),C)). [resolve(68,a,80,a)].
% 1.04/1.56 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(A,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)). [resolve(68,a,81,a)].
% 1.04/1.56 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(68,a,82,a)].
% 1.04/1.58 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(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(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(68,a,84,a)].
% 1.04/1.58 85 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.04/1.58 86 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = B | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 1.04/1.58 87 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) != B | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 1.04/1.58 88 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = C | -hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 1.04/1.58 89 -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].
% 1.04/1.58 90 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) # label(cls_le__infE_0) # label(axiom). [assumption].
% 1.04/1.58 91 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(D,C,A))) # label(cls_le__infE_1) # label(axiom). [assumption].
% 1.04/1.58 92 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 1.04/1.58 93 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 1.04/1.58 94 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 1.04/1.58 95 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(D,C,A))) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 1.04/1.58 96 -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].
% 1.04/1.58 97 -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].
% 1.04/1.58 98 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 1.04/1.58 99 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 1.04/1.58 100 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__infI_0) # label(axiom). [assumption].
% 1.04/1.58 101 -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].
% 1.04/1.58 102 -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].
% 1.04/1.58 103 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),C)) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 1.04/1.58 104 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),B)) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 1.04/1.58 105 -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].
% 1.04/1.58 106 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 1.04/1.58 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(D,A)),B),C)). [resolve(85,a,86,a)].
% 1.04/1.58 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) != B | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(D,A)),B),C)). [resolve(85,a,87,a)].
% 1.04/1.58 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = C | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(D,A)),C),B)). [resolve(85,a,88,a)].
% 1.04/1.58 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(85,a,89,a)].
% 1.04/1.58 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),c_Lattices_Olower__semilattice__class_Oinf(D,E,tc_fun(B,A)))). [resolve(85,a,90,a)].
% 1.04/1.58 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),c_Lattices_Olower__semilattice__class_Oinf(E,D,tc_fun(B,A)))). [resolve(85,a,91,a)].
% 1.04/1.58 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,A))),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)). [resolve(85,a,92,a)].
% 1.04/1.58 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,A))),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),D),E)). [resolve(85,a,93,a)].
% 1.04/1.58 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(85,a,96,a)].
% 1.04/1.58 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(85,a,97,a)].
% 1.04/1.58 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),c_Lattices_Olower__semilattice__class_Oinf(D,E,tc_fun(B,A)))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(85,a,98,a)].
% 1.04/1.58 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(85,a,101,a)].
% 1.04/1.58 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(85,a,102,a)].
% 1.04/1.58 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,A))),D)). [resolve(85,a,103,a)].
% 1.04/1.58 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,A))),C)). [resolve(85,a,104,a)].
% 1.04/1.58 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(85,a,105,a)].
% 1.04/1.58 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(85,a,106,a)].
% 1.04/1.58 107 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.04/1.58 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(107,a,86,a)].
% 1.04/1.58 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) != A | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(107,a,87,a)].
% 1.04/1.58 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(107,a,88,a)].
% 1.04/1.58 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_nat). [resolve(107,a,89,a)].
% 1.04/1.58 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat))). [resolve(107,a,90,a)].
% 1.04/1.58 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_nat))). [resolve(107,a,91,a)].
% 1.04/1.58 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(107,a,92,a)].
% 1.04/1.58 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)). [resolve(107,a,93,a)].
% 1.04/1.58 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(107,a,96,a)].
% 1.04/1.58 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(107,a,97,a)].
% 1.04/1.58 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(107,a,98,a)].
% 1.04/1.58 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(107,a,101,a)].
% 1.04/1.58 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(107,a,102,a)].
% 1.04/1.58 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat)),B)). [resolve(107,a,103,a)].
% 1.04/1.58 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat)),A)). [resolve(107,a,104,a)].
% 1.04/1.58 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(107,a,105,a)].
% 1.04/1.58 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_nat) = A. [resolve(107,a,106,a)].
% 1.04/1.58 108 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.04/1.59 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(108,a,86,a)].
% 1.04/1.59 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(108,a,87,a)].
% 1.04/1.59 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),A)). [resolve(108,a,88,a)].
% 1.04/1.59 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(108,a,89,a)].
% 1.04/1.59 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool))). [resolve(108,a,90,a)].
% 1.04/1.59 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_bool))). [resolve(108,a,91,a)].
% 1.04/1.59 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)). [resolve(108,a,92,a)].
% 1.04/1.59 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),C)). [resolve(108,a,93,a)].
% 1.04/1.59 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(108,a,96,a)].
% 1.04/1.59 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(108,a,97,a)].
% 1.04/1.59 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(108,a,98,a)].
% 1.04/1.59 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(108,a,101,a)].
% 1.04/1.59 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(108,a,102,a)].
% 1.04/1.59 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool)),B)). [resolve(108,a,103,a)].
% 1.04/1.59 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool)),A)). [resolve(108,a,104,a)].
% 1.04/1.59 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(108,a,105,a)].
% 1.04/1.59 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(108,a,106,a)].
% 1.04/1.59 109 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 1.04/1.59 110 -class_OrderedGroup_Omonoid__add(A) | c_List_Olistsum(c_List_Olist_ONil(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_listsum_Osimps_I1_J_0) # label(axiom). [assumption].
% 1.04/1.59 111 -class_OrderedGroup_Omonoid__add(A) | c_List_Olistsum(B,A) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),B,A,A) # label(cls_listsum_0) # label(axiom). [assumption].
% 1.04/1.59 112 -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].
% 1.04/1.59 113 -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].
% 1.04/1.59 114 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),C,A,A)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),B,C,A,A) # label(cls_foldl__absorb0_0) # label(axiom). [assumption].
% 1.04/1.66 115 -class_OrderedGroup_Omonoid__add(A) | c_List_Olistsum(c_List_Oappend(B,C,A),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_List_Olistsum(B,A)),c_List_Olistsum(C,A)) # label(cls_listsum__append_0) # label(axiom). [assumption].
% 1.04/1.66 Derived: c_List_Olistsum(c_List_Olist_ONil(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(109,a,110,a)].
% 1.04/1.66 Derived: c_List_Olistsum(A,tc_nat) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat,tc_nat). [resolve(109,a,111,a)].
% 1.04/1.66 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat,tc_nat)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat,tc_nat). [resolve(109,a,114,a)].
% 1.04/1.66 Derived: c_List_Olistsum(c_List_Oappend(A,B,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_List_Olistsum(A,tc_nat)),c_List_Olistsum(B,tc_nat)). [resolve(109,a,115,a)].
% 1.04/1.66 116 class_Ring__and__Field_Osemiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring) # label(axiom). [assumption].
% 1.04/1.66 117 -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].
% 1.04/1.66 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(116,a,117,a)].
% 1.04/1.66 118 class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) # label(axiom). [assumption].
% 1.04/1.66 119 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),E)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_add__mono_0) # label(axiom). [assumption].
% 1.04/1.66 120 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_add__right__mono_0) # label(axiom). [assumption].
% 1.04/1.66 121 -class_OrderedGroup_Opordered__ab__semigroup__add(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) # label(cls_add__left__mono_0) # label(axiom). [assumption].
% 1.04/1.66 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(118,a,119,a)].
% 1.04/1.66 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(118,a,120,a)].
% 1.04/1.66 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)). [resolve(118,a,121,a)].
% 1.04/1.66 122 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.04/1.66 123 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) # label(cls_of__nat__le__iff_1) # label(axiom). [assumption].
% 1.04/1.66 124 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A))) # label(cls_of__nat__le__iff_0) # label(axiom). [assumption].
% 1.04/1.66 125 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_HOL_Ozero__class_Ozero(A))) # label(cls_of__nat__less__0__iff_0) # label(axiom). [assumption].
% 1.04/1.66 126 -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].
% 1.04/1.66 127 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A))) # label(cls_of__nat__0__le__iff_0) # label(axiom). [assumption].
% 1.04/1.66 128 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A))) # label(cls_zero__le__imp__of__nat_0) # label(axiom). [assumption].
% 1.04/1.66 129 -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].
% 1.04/1.66 130 -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].
% 1.04/1.66 131 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Oone__class_Oone(A))) # label(cls_zero__le__one_0) # label(axiom). [assumption].
% 1.04/1.66 132 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Oone__class_Oone(A)),c_HOL_Ozero__class_Ozero(A))) # label(cls_not__one__le__zero_0) # label(axiom). [assumption].
% 1.04/1.66 133 -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].
% 1.04/1.66 134 -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].
% 1.04/1.66 135 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),A),c_Nat_Osemiring__1__class_Oof__nat(B,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),B)) # label(cls_of__nat__0__less__iff_1) # label(axiom). [assumption].
% 1.04/1.66 136 -class_Ring__and__Field_Oordered__semidom(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(A),A),c_Nat_Osemiring__1__class_Oof__nat(B,A))) # label(cls_of__nat__0__less__iff_0) # label(axiom). [assumption].
% 1.04/1.66 137 -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].
% 1.04/1.66 138 -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(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_Nat_Osemiring__1__class_Oof__nat(C,A))) # label(cls_of__nat__less__iff_0) # label(axiom). [assumption].
% 1.04/1.66 139 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),A),c_Nat_Osemiring__1__class_Oof__nat(C,A))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),C)) # label(cls_of__nat__less__iff_1) # label(axiom). [assumption].
% 1.04/1.69 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(122,a,123,a)].
% 1.04/1.69 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))). [resolve(122,a,124,a)].
% 1.04/1.69 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(122,a,125,a)].
% 1.04/1.69 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(122,a,126,a)].
% 1.04/1.69 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat))). [resolve(122,a,127,a)].
% 1.04/1.69 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(122,a,129,a)].
% 1.04/1.69 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(122,a,130,a)].
% 1.04/1.69 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))). [resolve(122,a,131,a)].
% 1.04/1.69 Derived: -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(122,a,132,a)].
% 1.04/1.69 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(122,a,133,a)].
% 1.04/1.69 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(122,a,134,a)].
% 1.04/1.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),A)). [resolve(122,a,135,a)].
% 1.04/1.69 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),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat))). [resolve(122,a,136,a)].
% 1.04/1.69 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(122,a,137,a)].
% 1.04/1.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))). [resolve(122,a,138,a)].
% 1.04/1.69 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)). [resolve(122,a,139,a)].
% 1.04/1.69 140 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 1.04/1.69 141 -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].
% 1.04/1.69 142 -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].
% 1.04/1.69 143 class_OrderedGroup_Ocomm__monoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__mult) # label(axiom). [assumption].
% 1.04/1.69 144 -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].
% 1.04/1.75 145 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 1.04/1.75 146 -class_Nat_Osemiring__char__0(A) | c_Nat_Osemiring__1__class_Oof__nat(B,A) != c_Nat_Osemiring__1__class_Oof__nat(C,A) | B = C # label(cls_of__nat__eq__iff_0) # label(axiom). [assumption].
% 1.04/1.75 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(145,a,146,a)].
% 1.04/1.75 147 class_Ring__and__Field_Oordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semiring) # label(axiom). [assumption].
% 1.04/1.75 148 -class_Ring__and__Field_Oordered__semiring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(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].
% 1.04/1.75 149 -class_Ring__and__Field_Oordered__semiring(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(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].
% 1.04/1.75 150 class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) # label(axiom). [assumption].
% 1.04/1.75 151 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_split__mult__neg__le_0) # label(axiom). [assumption].
% 1.04/1.75 152 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_split__mult__neg__le_1) # label(axiom). [assumption].
% 1.04/1.75 153 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_mult__nonneg__nonpos_0) # label(axiom). [assumption].
% 1.04/1.75 154 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_HOL_Ozero__class_Ozero(A))) # label(cls_mult__nonpos__nonneg_0) # label(axiom). [assumption].
% 1.04/1.75 155 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_HOL_Ozero__class_Ozero(A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) # label(cls_mult__nonneg__nonpos2_0) # label(axiom). [assumption].
% 1.04/1.75 156 -class_Ring__and__Field_Opordered__cancel__semiring(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) # label(cls_mult__nonneg__nonneg_0) # label(axiom). [assumption].
% 1.04/1.75 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(150,a,151,a)].
% 1.04/1.75 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),c_HOL_Ozero__class_Ozero(tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(150,a,152,a)].
% 1.53/1.79 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(150,a,156,a)].
% 1.53/1.79 157 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.53/1.79 158 -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].
% 1.53/1.79 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(157,a,158,a)].
% 1.53/1.79 159 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 1.53/1.79 160 -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].
% 1.53/1.79 161 -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].
% 1.53/1.79 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(159,a,161,a)].
% 1.53/1.79 162 class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) # label(axiom). [assumption].
% 1.53/1.79 163 -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].
% 1.53/1.79 164 class_Ring__and__Field_Opordered__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Opordered__semiring) # label(axiom). [assumption].
% 1.53/1.79 165 -class_Ring__and__Field_Opordered__semiring(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),E)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_mult__mono_0) # label(axiom). [assumption].
% 1.53/1.79 166 -class_Ring__and__Field_Opordered__semiring(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),E)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_mult__mono_H_0) # label(axiom). [assumption].
% 1.53/1.79 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(164,a,165,a)].
% 1.53/1.79 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(164,a,166,a)].
% 1.53/1.81 167 class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) # label(axiom). [assumption].
% 1.53/1.81 168 -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(hAPP(c_lessequals(A),B),D)) # label(cls_add__le__less__mono_0) # label(axiom). [assumption].
% 1.53/1.81 169 -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(hAPP(c_lessequals(A),C),E)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),D)) # label(cls_add__less__le__mono_0) # label(axiom). [assumption].
% 1.53/1.81 170 -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].
% 1.53/1.81 171 -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].
% 1.53/1.81 172 -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].
% 1.53/1.81 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(hAPP(c_lessequals(tc_nat),A),C)). [resolve(167,a,168,a)].
% 1.53/1.81 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(hAPP(c_lessequals(tc_nat),B),D)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),C)). [resolve(167,a,169,a)].
% 1.53/1.81 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(167,a,170,a)].
% 1.53/1.81 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(167,a,171,a)].
% 1.53/1.81 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(167,a,172,a)].
% 1.53/1.81 173 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.53/1.81 174 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 1.53/1.81 175 -class_Orderings_Olinorder(A) | B = C | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 1.53/1.81 176 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_not__leE_0) # label(axiom). [assumption].
% 1.53/1.81 177 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),B)) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 1.57/1.82 178 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),B)) | hBOOL(hAPP(hAPP(c_lessequals(A),B),B)) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 1.57/1.82 179 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 1.57/1.82 180 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 1.57/1.82 181 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(C,A),B)) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 1.57/1.82 182 -class_Orderings_Olinorder(A) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 1.57/1.82 183 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 1.57/1.82 184 -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].
% 1.57/1.82 185 -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].
% 1.57/1.82 186 -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].
% 1.57/1.82 187 -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].
% 1.57/1.82 188 -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].
% 1.57/1.82 189 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,A),B)) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.57/1.82 Derived: A = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(173,a,174,a)].
% 1.57/1.82 Derived: hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(173,a,176,a)].
% 1.57/1.82 Derived: -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),A)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),A)). [resolve(173,a,177,a)].
% 1.57/1.82 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(173,a,179,a)].
% 1.57/1.82 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(173,a,183,a)].
% 1.57/1.82 Derived: -hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | -hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),A)). [resolve(173,a,184,a)].
% 1.57/1.82 Derived: A = B | hBOOL(hAPP(c_HOL_Oord__class_Oless(A,tc_nat),B)) | hBOOL(hAPP(c_HOL_Oord__class_Oless(B,tc_nat),A)). [resolve(173,a,185,a)].
% 1.57/1.82 190 class_Ring__and__Field_Ono__zero__divisors(tc_nat) # label(clsarity_nat__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 1.57/1.82 191 -class_Ring__and__Field_Ono__zero__divisors(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) != c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_no__zero__divisors_0) # label(axiom). [assumption].
% 1.57/1.82 192 -class_Ring__and__Field_Ono__zero__divisors(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) | C = c_HOL_Ozero__class_Ozero(A) # label(cls_no__zero__divirors__neq0_0) # label(axiom). [assumption].
% 1.57/1.82 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) != c_HOL_Ozero__class_Ozero(tc_nat) | B = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(190,a,191,a)].
% 1.59/1.86 193 class_Ring__and__Field_Omult__zero(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__zero) # label(axiom). [assumption].
% 1.59/1.86 194 -class_Ring__and__Field_Omult__zero(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__zero__right_0) # label(axiom). [assumption].
% 1.59/1.86 195 -class_Ring__and__Field_Omult__zero(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__zero__left_0) # label(axiom). [assumption].
% 1.59/1.86 196 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.59/1.86 197 -class_Ring__and__Field_Osemiring__0(A) | c_List_Olistsum(c_List_Omap(hAPP(hAPP(c_COMBB(A,A,B),hAPP(c_HOL_Otimes__class_Otimes(A),C)),D),E,B,A),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),c_List_Olistsum(c_List_Omap(D,E,B,A),A)) # label(cls_listsum__const__mult_0) # label(axiom). [assumption].
% 1.59/1.86 198 -class_Ring__and__Field_Osemiring__0(A) | c_List_Olistsum(c_List_Omap(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Otimes__class_Otimes(A)),C),B,A,A),D),E,B,A),A) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_List_Olistsum(c_List_Omap(C,E,B,A),A)),D) # label(cls_listsum__mult__const_0) # label(axiom). [assumption].
% 1.59/1.86 Derived: c_List_Olistsum(c_List_Omap(hAPP(hAPP(c_COMBB(tc_nat,tc_nat,A),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B)),C),D,A,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),c_List_Olistsum(c_List_Omap(C,D,A,tc_nat),tc_nat)). [resolve(196,a,197,a)].
% 1.59/1.86 Derived: c_List_Olistsum(c_List_Omap(hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),A),c_HOL_Otimes__class_Otimes(tc_nat)),B),A,tc_nat,tc_nat),C),D,A,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_List_Olistsum(c_List_Omap(B,D,A,tc_nat),tc_nat)),C). [resolve(196,a,198,a)].
% 1.59/1.86 199 class_OrderedGroup_Osemigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 1.59/1.86 200 -class_OrderedGroup_Osemigroup__add(A) | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),C,D,A,A)) # label(cls_foldl__assoc_0) # label(axiom). [assumption].
% 1.59/1.86 Derived: c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),B,C,tc_nat,tc_nat)). [resolve(199,a,200,a)].
% 1.59/1.86 201 class_Ring__and__Field_Omult__mono(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono) # label(axiom). [assumption].
% 1.59/1.86 202 -class_Ring__and__Field_Omult__mono(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_mult__right__mono_0) # label(axiom). [assumption].
% 1.59/1.86 203 -class_Ring__and__Field_Omult__mono(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) # label(cls_mult__left__mono_0) # label(axiom). [assumption].
% 1.59/1.86 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(201,a,202,a)].
% 1.59/1.86 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)). [resolve(201,a,203,a)].
% 2.18/2.49 204 class_Ring__and__Field_Omult__mono1(tc_nat) # label(clsarity_nat__Ring__and__Field_Omult__mono1) # label(axiom). [assumption].
% 2.18/2.49 205 -class_Ring__and__Field_Omult__mono1(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_HOL_Ozero__class_Ozero(A)),B)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) # label(cls_mult__mono1_0) # label(axiom). [assumption].
% 2.18/2.49 206 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 2.18/2.49 207 -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].
% 2.18/2.49 208 class_Ring__and__Field_Ocomm__semiring(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring) # label(axiom). [assumption].
% 2.18/2.49 209 -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].
% 2.18/2.49
% 2.18/2.49 ============================== end predicate elimination =============
% 2.18/2.49
% 2.18/2.49 Auto_denials: (non-Horn, no changes).
% 2.18/2.49
% 2.18/2.49 Term ordering decisions:
% 2.18/2.49 Function symbol KB weights: tc_nat=1. tc_bool=1. tc_Lambda_OdB=1. c_Lambda_OdB_OApp=1. c_Lambda_Osubst=1. c_Lambda_Olift=1. t_a=1. c_InductTermi_OIT=1. c_Lambda_Obeta=1. c_and=1. v_x=1. tc_Type_Otype=1. c_or=1. v_P=1. v_n=1. c_implies=1. v_ia=1. v_rs=1. hAPP=1. c_HOL_Oord__class_Oless=1. tc_fun=1. c_Nat_Osemiring__1__class_Oof__nat=1. c_Collect=1. c_List_Olistsum=1. c_Hilbert__Choice_OEps=1. c_The=1. c_lessequals=1. c_HOL_Oplus__class_Oplus=1. c_HOL_Ozero__class_Ozero=1. c_HOL_Otimes__class_Otimes=1. c_Suc=1. c_List_Olist_ONil=1. c_Lambda_OdB_OVar=1. c_Lambda_OdB_OAbs=1. c_HOL_Oone__class_Oone=1. c_Orderings_Obot__class_Obot=1. c_fequal=1. v_sko__InductTermi__XIT__Xcases__1=1. v_sko__InductTermi__XIT__Xcases__3=1. v_sko__InductTermi__XIT__Xcases__5=1. c_All=1. v_sko__InductTermi__XIT__Xcases__2=1. c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1=1. c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2=1. c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3=1. c_ListApplication_Osko__ListApplication__Xlem__1__1=1. c_ListApplication_Osko__ListApplication__Xlem__1__2=1. c_ListApplication_Osko__ListApplication__Xlem__1__3=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_List_Oappend=1. c_COMBB=1. c_List_Olistsp=1. c_Lambda_Oliftn=1. c_Lambda_Osubstn=1. c_List_Ofilter=1. c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1=1. c_List_Osko__List__Xin__listsp__conv__set__1__1=1. c_Orderings_Oord_OLeast=1. c_List_Omap=1. c_COMBS=1. c_COMBC=1. c_Type_Oshift=1. c_List_Osko__List__Xfoldl__apply__inv__1__1=1. c_Hilbert__Choice_OGreatestM=1. c_Type_Osko__Type__Xvar__app__typesE__1__1=1. c_Type_Osko__Type__Xvar__app__types__1__1=1. c_List_Ofoldl=1. c_Lambda_OdB_OdB__case=1. c_Lambda_OdB_OdB__rec=1.
% 2.18/2.49
% 2.18/2.49 ============================== end of process initial clauses ========
% 2.18/2.49
% 2.18/2.49 ============================== CLAUSES FOR SEARCH ====================
% 2.18/2.49
% 2.18/2.49 ============================== end of clauses for search =============
% 2.18/2.49
% 2.18/2.49 ============================== SEARCH ================================
% 2.18/2.49
% 2.18/2.49 % Starting search at 0.64 seconds.
% 2.18/2.49
% 2.18/2.49 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 47 (0.00 of 1.07 sec).
% 2.18/2.49
% 2.18/2.49 Low Water (keep): wt=56.000, iters=3486
% 2.18/2.49
% 2.18/2.49 Low Water (keep): wt=47.000, iters=3343
% 2.18/2.49
% 2.18/2.49 Low Water (keep): wt=43.000, iters=3355
% 2.18/2.49
% 2.18/2.49 Low Water (keep): wt=41.000, iters=3358
% 2.18/2.49
% 2.18/2.49 Low Water (keep): wt=39.000, iters=3351
% 2.18/2.49
% 2.18/2.49 Low Water (keep): wt=38.000, iters=3552
% 2.18/2.49
% 2.18/2.49 Low Water (keep): wt=36.000, iters=3369
% 2.18/2.49
% 2.18/2.49 Low Water (keep): wt=Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------