%------------------------------------------------------------------------------
% File : SOS---2.0
% Problem : SWV575-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : sos-script %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 21:39:31 EDT 2022
% Result : Unknown 0.52s 0.74s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV575-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : sos-script %s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Wed Jun 15 01:35:18 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.60 ----- Otter 3.2, August 2001 -----
% 0.21/0.60 The process was started by sandbox2 on n024.cluster.edu,
% 0.21/0.60 Wed Jun 15 01:35:18 2022
% 0.21/0.60 The command was "./sos". The process ID is 5769.
% 0.21/0.60
% 0.21/0.60 set(prolog_style_variables).
% 0.21/0.60 set(auto).
% 0.21/0.60 dependent: set(auto1).
% 0.21/0.60 dependent: set(process_input).
% 0.21/0.60 dependent: clear(print_kept).
% 0.21/0.60 dependent: clear(print_new_demod).
% 0.21/0.60 dependent: clear(print_back_demod).
% 0.21/0.60 dependent: clear(print_back_sub).
% 0.21/0.60 dependent: set(control_memory).
% 0.21/0.60 dependent: assign(max_mem, 12000).
% 0.21/0.60 dependent: assign(pick_given_ratio, 4).
% 0.21/0.60 dependent: assign(stats_level, 1).
% 0.21/0.60 dependent: assign(pick_semantic_ratio, 3).
% 0.21/0.60 dependent: assign(sos_limit, 5000).
% 0.21/0.60 dependent: assign(max_weight, 60).
% 0.21/0.60 clear(print_given).
% 0.21/0.60
% 0.21/0.60 list(usable).
% 0.21/0.60
% 0.21/0.60 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 0.21/0.60
% 0.21/0.60 This ia a non-Horn set with equality. The strategy will be
% 0.21/0.60 Knuth-Bendix, ordered hyper_res, ur_res, factoring, and
% 0.21/0.60 unit deletion, with positive clauses in sos and nonpositive
% 0.21/0.60 clauses in usable.
% 0.21/0.60
% 0.21/0.60 dependent: set(knuth_bendix).
% 0.21/0.60 dependent: set(para_from).
% 0.21/0.60 dependent: set(para_into).
% 0.21/0.60 dependent: clear(para_from_right).
% 0.21/0.60 dependent: clear(para_into_right).
% 0.21/0.60 dependent: set(para_from_vars).
% 0.21/0.60 dependent: set(eq_units_both_ways).
% 0.21/0.60 dependent: set(dynamic_demod_all).
% 0.21/0.60 dependent: set(dynamic_demod).
% 0.21/0.60 dependent: set(order_eq).
% 0.21/0.60 dependent: set(back_demod).
% 0.21/0.60 dependent: set(lrpo).
% 0.21/0.60 dependent: set(hyper_res).
% 0.21/0.60 dependent: set(unit_deletion).
% 0.21/0.60 dependent: set(factor).
% 0.21/0.60
% 0.21/0.60 ------------> process usable:
% 0.21/0.60 Following clause subsumed by 13 during input processing: 0 [flip.3] {-} -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),C,A)=B|C=c_HOL_Ozero__class_Ozero(A).
% 0.21/0.60 Following clause subsumed by 15 during input processing: 0 [flip.3] {-} -class_Ring__and__Field_Ofield(A)|B=c_HOL_Ozero__class_Ozero(A)|c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B),B,A)=C.
% 0.21/0.60 Following clause subsumed by 21 during input processing: 0 [] {-} -class_Orderings_Oorder(A)|B=C| -c_lessequals(C,B,A)| -c_lessequals(B,C,A).
% 0.21/0.60 Following clause subsumed by 21 during input processing: 0 [] {-} -class_Orderings_Oorder(A)|B=C| -c_lessequals(B,C,A)| -c_lessequals(C,B,A).
% 0.21/0.60 Following clause subsumed by 22 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|C=B|c_HOL_Oord__class_Oless(C,B,A).
% 0.21/0.60 Following clause subsumed by 22 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A).
% 0.21/0.60 Following clause subsumed by 22 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(C,B,A)|c_HOL_Oord__class_Oless(B,C,A).
% 0.21/0.60 Following clause subsumed by 52 during input processing: 0 [] {-} hBOOL(hAPP(hAPP(A,hAPP(hAPP(c_Power_Opower_Opower(B,C,D),E),F)),hAPP(hAPP(c_Power_Opower_Opower(B,C,D),E),G)))| -hBOOL(hAPP(hAPP(A,B),E))| -c_HOL_Oord__class_Oless(F,G,tc_nat)| -c_Ring__and__Field_Oordered__semidom(H,I,B,C,J,A,D).
% 0.21/0.60 Following clause subsumed by 53 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(A,B,tc_nat)| -hBOOL(hAPP(hAPP(C,hAPP(hAPP(c_Power_Opower_Opower(D,E,F),G),A)),hAPP(hAPP(c_Power_Opower_Opower(D,E,F),G),B)))| -hBOOL(hAPP(hAPP(C,D),G))| -c_Ring__and__Field_Oordered__semidom(H,I,D,E,J,C,F).
% 0.21/0.60 Following clause subsumed by 99 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lessequals(B,c_HOL_Oinverse__class_Odivide(C,D,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A)| -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),C,A).
% 0.21/0.60 Following clause subsumed by 100 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lessequals(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A).
% 0.21/0.60 Following clause subsumed by 49 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oinverse__class_Odivide(C,D,A),A)| -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A)| -c_lessequals(C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D),A)| -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D),C,A).
% 0.21/0.60 Following clause subsumed by 119 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 0.21/0.60 Following clause subsumed by 120 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 0.21/0.60 Following clause subsumed by 171 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A).
% 0.21/0.60 Following clause subsumed by 202 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C),D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oinverse__class_Odivide(D,C,A),A).
% 0.21/0.60 Following clause subsumed by 205 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oinverse__class_Odivide(C,D,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D),C,A).
% 0.21/0.60 Following clause subsumed by 99 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oinverse__class_Odivide(C,D,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A)| -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D),C,A).
% 0.21/0.60 Following clause subsumed by 101 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C),D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oinverse__class_Odivide(D,C,A),A).
% 0.21/0.60 Following clause subsumed by 232 during input processing: 0 [] {-} -class_Ring__and__Field_Ofield(A)| -class_Int_Onumber__ring(A)|c_HOL_Oinverse__class_Oinverse(B,A)=c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A).
% 0.21/0.60 Following clause subsumed by 248 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oone__class_Oone(A)),B)=B.
% 0.21/0.60 Following clause subsumed by 259 during input processing: 0 [] {-} -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)).
% 0.21/0.61 Following clause subsumed by 269 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 0.21/0.61 Following clause subsumed by 275 during input processing: 0 [] {-} -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).
% 0.21/0.61 Following clause subsumed by 199 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)|c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat).
% 0.21/0.61 Following clause subsumed by 285 during input processing: 0 [flip.2] {-} -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)).
% 0.21/0.61 Following clause subsumed by 285 during input processing: 0 [] {-} -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)).
% 0.21/0.61 Following clause subsumed by 295 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,B,A)|c_lessequals(B,B,A).
% 0.21/0.61 Following clause subsumed by 295 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_lessequals(B,C,A)|c_HOL_Oord__class_Oless(C,B,A).
% 0.21/0.61 Following clause subsumed by 295 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_lessequals(C,B,A).
% 0.21/0.61 Following clause subsumed by 297 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)| -c_lessequals(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 0.21/0.61 Following clause subsumed by 298 during input processing: 0 [] {-} -class_Ring__and__Field_Ofield(A)|c_HOL_Oinverse__class_Odivide(B,B,A)=c_HOL_Oone__class_Oone(A)|B=c_HOL_Ozero__class_Ozero(A).
% 0.21/0.61 Following clause subsumed by 298 during input processing: 0 [] {-} -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Odivide(B,B,A)=c_HOL_Oone__class_Oone(A)|B=c_HOL_Ozero__class_Ozero(A).
% 0.21/0.61 Following clause subsumed by 300 during input processing: 0 [] {-} -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A).
% 0.21/0.61 Following clause subsumed by 302 during input processing: 0 [] {-} -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,C,A)),D),C,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A).
% 0.21/0.61 Following clause subsumed by 322 during input processing: 0 [] {-} -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Odiv(B,C,A)),C)),c_Divides_Odiv__class_Omod(B,C,A))=B.
% 0.21/0.61 Following clause subsumed by 324 during input processing: 0 [] {-} -class_Orderings_Oorder(A)|B=C|c_HOL_Oord__class_Oless(B,C,A)| -c_lessequals(B,C,A).
% 0.21/0.61 Following clause subsumed by 324 during input processing: 0 [] {-} -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)|B=C| -c_lessequals(B,C,A).
% 0.21/0.61 Following clause subsumed by 324 during input processing: 0 [] {-} -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_lessequals(B,C,A)|B=C.
% 0.21/0.61 Following clause subsumed by 325 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(B,C,A)| -c_lessequals(B,C,A).
% 0.21/0.61 Following clause subsumed by 326 during input processing: 0 [] {-} -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)|C=B| -c_lessequals(B,C,A).
% 0.21/0.61 Following clause subsumed by 334 during input processing: 0 [] {-} -class_Ring__and__Field_Opordered__ring(A)|c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A)| -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A).
% 0.21/0.61 Following clause subsumed by 127 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)| -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(B,tc_nat)),c_HOL_Ozero__class_Ozero(A),A).
% 0.21/0.61 Following clause subsumed by 349 during input processing: 0 [flip.2] {-} -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)).
% 0.21/0.61 Following clause subsumed by 349 during input processing: 0 [flip.2] {-} -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)).
% 0.21/0.61 Following clause subsumed by 353 during input processing: 0 [flip.2] {-} -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 0.21/0.61 Following clause subsumed by 354 during input processing: 0 [] {-} -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)).
% 0.21/0.61 Following clause subsumed by 120 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 0.21/0.61 Following clause subsumed by 119 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 0.21/0.61 Following clause subsumed by 100 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),c_Int_Onumber__class_Onumber__of(D,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lessequals(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(D,A)),C),A).
% 0.21/0.61 Following clause subsumed by 102 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lessequals(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(C,A)),D),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A)| -c_lessequals(c_HOL_Oinverse__class_Odivide(B,D,A),c_Int_Onumber__class_Onumber__of(C,A),A).
% 0.21/0.61 Following clause subsumed by 232 during input processing: 0 [] {-} -class_Ring__and__Field_Ofield(A)|c_HOL_Oinverse__class_Oinverse(B,A)=c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A)|B=c_HOL_Ozero__class_Ozero(A).
% 0.21/0.61 Following clause subsumed by 382 during input processing: 0 [] {-} -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ouminus__class_Ouminus(B,A)),C)=c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A).
% 0.21/0.61 Following clause subsumed by 383 during input processing: 0 [] {-} -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ouminus__class_Ouminus(C,A))=c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),A).
% 0.21/0.61 Following clause subsumed by 417 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A)| -c_Parity_Oeven__odd__class_Oeven(C,tc_nat).
% 0.21/0.61 Following clause subsumed by 425 during input processing: 0 [] {-} -class_OrderedGroup_Ogroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ouminus__class_Ouminus(B,A)),B)=c_HOL_Ozero__class_Ozero(A).
% 0.21/0.61 Following clause subsumed by 434 during input processing: 0 [] {-} -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ominus__class_Ominus(C,D,A))=c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A).
% 0.21/0.61 Following clause subsumed by 435 during input processing: 0 [] {-} -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ominus__class_Ominus(B,C,A)),D)=c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D),A).
% 0.21/0.61 Following clause subsumed by 144 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,C)),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,C)),B),tc_nat).
% 0.21/0.61 Following clause subsumed by 205 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(C,c_Int_Onumber__class_Onumber__of(D,A),A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(D,A),A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(D,A)),C,A).
% 0.21/0.61 Following clause subsumed by 202 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(C,A)),D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(C,A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(D,c_Int_Onumber__class_Onumber__of(C,A),A),A).
% 0.21/0.61 Following clause subsumed by 204 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(C,A),A),D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(C,A),A)| -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),c_Int_Onumber__class_Onumber__of(C,A)),A).
% 0.21/0.61 Following clause subsumed by 200 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),c_Int_Onumber__class_Onumber__of(D,A)),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(D,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(D,A),A),C,A).
% 0.21/0.61 Following clause subsumed by 456 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Oinverse(B,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 0.21/0.61 Following clause subsumed by 233 during input processing: 0 [flip.2] {-} -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Divides_Odiv__class_Omod(B,D,A)),C),D,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),D,A).
% 0.21/0.61 Following clause subsumed by 491 during input processing: 0 [] {-} c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(B,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(A,tc_nat).
% 0.21/0.61 Following clause subsumed by 493 during input processing: 0 [] {-} c_Parity_Oeven__odd__class_Oeven(A,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(B,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat).
% 0.21/0.61 Following clause subsumed by 492 during input processing: 0 [] {-} c_Parity_Oeven__odd__class_Oeven(A,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(B,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A),tc_nat).
% 0.21/0.61 Following clause subsumed by 492 during input processing: 0 [] {-} -c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat)|c_Parity_Oeven__odd__class_Oeven(B,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(A,tc_nat).
% 0.21/0.61 Following clause subsumed by 493 during input processing: 0 [] {-} -c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(B,tc_nat)|c_Parity_Oeven__odd__class_Oeven(A,tc_nat).
% 0.21/0.61 Following clause subsumed by 491 during input processing: 0 [] {-} -c_Parity_Oeven__odd__class_Oeven(A,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(B,tc_nat)|c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A),tc_nat).
% 0.21/0.61 Following clause subsumed by 502 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 0.21/0.61 Following clause subsumed by 501 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 0.21/0.61 Following clause subsumed by 517 during input processing: 0 [flip.2] {-} -class_OrderedGroup_Oab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ouminus__class_Ouminus(C,A))=c_HOL_Ominus__class_Ominus(B,C,A).
% 0.21/0.61 Following clause subsumed by 542 during input processing: 0 [flip.1] {-} hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_Groebner__Basis_Ogb__semiring(E,A,F,G,H,I).
% 0.21/0.61 Following clause subsumed by 545 during input processing: 0 [flip.1] {-} hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_Groebner__Basis_Ogb__semiring(A,E,F,G,H,I).
% 0.21/0.61 Following clause subsumed by 530 during input processing: 0 [] {-} hAPP(hAPP(A,B),C)=C| -c_Groebner__Basis_Ogb__semiring(A,D,E,B,F,G).
% 0.21/0.61 Following clause subsumed by 545 during input processing: 0 [flip.1] {-} hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_Groebner__Basis_Ogb__semiring(A,E,F,G,H,I).
% 0.21/0.61 Following clause subsumed by 548 during input processing: 0 [] {-} hAPP(hAPP(A,B),C)=hAPP(hAPP(A,C),B)| -c_Groebner__Basis_Ogb__semiring(A,D,E,F,G,H).
% 0.21/0.61 Following clause subsumed by 534 during input processing: 0 [] {-} hAPP(hAPP(A,B),C)=B| -c_Groebner__Basis_Ogb__semiring(D,A,E,B,F,G).
% 0.21/0.61 Following clause subsumed by 536 during input processing: 0 [] {-} hAPP(hAPP(A,B),C)=C| -c_Groebner__Basis_Ogb__semiring(D,A,E,F,B,G).
% 0.21/0.61 Following clause subsumed by 542 during input processing: 0 [flip.1] {-} hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_Groebner__Basis_Ogb__semiring(E,A,F,G,H,I).
% 0.21/0.61 Following clause subsumed by 532 during input processing: 0 [] {-} hAPP(hAPP(A,B),C)=hAPP(hAPP(A,C),B)| -c_Groebner__Basis_Ogb__semiring(D,A,E,F,G,H).
% 0.21/0.61 Following clause subsumed by 559 during input processing: 0 [] {-} -class_OrderedGroup_Opordered__ab__group__add__abs(A)|c_lessequals(c_HOL_Oabs__class_Oabs(B,A),C,A)| -c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A)| -c_lessequals(B,C,A).
% 0.21/0.61 Following clause subsumed by 562 during input processing: 0 [] {-} hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)|B=C.
% 0.21/0.61 Following clause subsumed by 99 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lessequals(B,c_HOL_Oinverse__class_Odivide(C,c_Int_Onumber__class_Onumber__of(D,A),A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(D,A),A)| -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(D,A)),C,A).
% 0.21/0.61 Following clause subsumed by 101 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(C,A)),D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(C,A),A)| -c_lessequals(B,c_HOL_Oinverse__class_Odivide(D,c_Int_Onumber__class_Onumber__of(C,A),A),A).
% 0.21/0.61 Following clause subsumed by 100 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lessequals(c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(C,A),A),D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(C,A),A)| -c_lessequals(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),c_Int_Onumber__class_Onumber__of(C,A)),A).
% 0.21/0.61 Following clause subsumed by 102 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lessequals(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),c_Int_Onumber__class_Onumber__of(D,A)),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(D,A),A)| -c_lessequals(c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(D,A),A),C,A).
% 0.21/0.61 Following clause subsumed by 584 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(D,B,A).
% 0.21/0.61 Following clause subsumed by 587 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(D,C,A).
% 0.21/0.61 Following clause subsumed by 588 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A)| -c_HOL_Oord__class_Oless(C,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 0.21/0.61 Following clause subsumed by 587 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D),A)| -c_HOL_Oord__class_Oless(D,C,A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 0.21/0.61 Following clause subsumed by 144 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat).
% 0.21/0.61 Following clause subsumed by 592 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 0.21/0.61 Following clause subsumed by 592 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C),tc_nat)| -c_HOL_Oord__class_Oless(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 0.43/0.62 Following clause subsumed by 593 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 0.43/0.62 Following clause subsumed by 616 during input processing: 0 [flip.2] {-} -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A)=B.
% 0.43/0.62 Following clause subsumed by 616 during input processing: 0 [flip.2] {-} -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A)=B.
% 0.43/0.62 Following clause subsumed by 616 during input processing: 0 [] {-} -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A)=B.
% 0.43/0.62 Following clause subsumed by 622 during input processing: 0 [] {-} -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(B,A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(C,A),B,A).
% 0.43/0.62 Following clause subsumed by 623 during input processing: 0 [] {-} -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ouminus__class_Ouminus(C,A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ouminus__class_Ouminus(B,A),A).
% 0.43/0.62 Following clause subsumed by 624 during input processing: 0 [] {-} -class_OrderedGroup_Opordered__ab__group__add(A)|c_lessequals(c_HOL_Ouminus__class_Ouminus(B,A),C,A)| -c_lessequals(c_HOL_Ouminus__class_Ouminus(C,A),B,A).
% 0.43/0.62 Following clause subsumed by 625 during input processing: 0 [] {-} -class_OrderedGroup_Opordered__ab__group__add(A)|c_lessequals(B,c_HOL_Ouminus__class_Ouminus(C,A),A)| -c_lessequals(C,c_HOL_Ouminus__class_Ouminus(B,A),A).
% 0.43/0.62 Following clause subsumed by 634 during input processing: 0 [] {-} -class_Ring__and__Field_Odivision__ring(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Oinverse(B,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 0.43/0.62 Following clause subsumed by 633 during input processing: 0 [flip.2] {-} -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 0.43/0.62 Following clause subsumed by 641 during input processing: 0 [] {-} -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Ozero__class_Ozero(A))=c_HOL_Ozero__class_Ozero(A).
% 0.43/0.62 Following clause subsumed by 642 during input processing: 0 [] {-} -class_RealVector_Oreal__normed__algebra(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B)=c_HOL_Ozero__class_Ozero(A).
% 0.43/0.62 Following clause subsumed by 640 during input processing: 0 [] {-} -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).
% 0.43/0.62 Following clause subsumed by 649 during input processing: 0 [] {-} -class_Ring__and__Field_Opordered__cancel__semiring(A)|c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A)| -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A).
% 0.43/0.62 Following clause subsumed by 650 during input processing: 0 [] {-} -class_Ring__and__Field_Opordered__cancel__semiring(A)|c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A)| -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A).
% 0.43/0.62 Following clause subsumed by 650 during input processing: 0 [] {-} -class_Ring__and__Field_Opordered__cancel__semiring(A)|c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C),c_HOL_Ozero__class_Ozero(A),A)| -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A).
% 0.43/0.62 Following clause subsumed by 200 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(C,A)),D),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A)| -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,D,A),c_Int_Onumber__class_Onumber__of(C,A),A).
% 0.43/0.62 Following clause subsumed by 204 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_Int_Onumber__class_Onumber__of(D,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(D,A)),C),A).
% 0.43/0.62 Following clause subsumed by 50 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lessequals(c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(C,A),A),D,A)| -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),c_Int_Onumber__class_Onumber__of(C,A)),B,A)| -c_lessequals(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),c_Int_Onumber__class_Onumber__of(C,A)),A).
% 0.43/0.62 Following clause subsumed by 49 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lessequals(B,c_HOL_Oinverse__class_Odivide(C,c_Int_Onumber__class_Onumber__of(D,A),A),A)| -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(D,A),c_HOL_Ozero__class_Ozero(A),A)| -c_lessequals(C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(D,A)),A)| -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(D,A)),C,A).
% 0.43/0.62 Following clause subsumed by 417 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A)| -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat).
% 0.43/0.62 Following clause subsumed by 694 during input processing: 0 [] {-} -hBOOL(hAPP(A,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),B,tc_nat)))|hBOOL(hAPP(A,C)).
% 0.43/0.62 Following clause subsumed by 220 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|B=c_HOL_Ozero__class_Ozero(A)| -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat)| -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),c_HOL_Ozero__class_Ozero(A),A).
% 0.43/0.62 Following clause subsumed by 128 during input processing: 0 [flip.2] {-} -class_Ring__and__Field_Oring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),E),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ominus__class_Ominus(B,E,A)),C)),D))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D).
% 0.43/0.62 Following clause subsumed by 50 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),c_Int_Onumber__class_Onumber__of(D,A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(D,A)),C),B,A)| -c_lessequals(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(D,A)),C),A).
% 0.43/0.62 Following clause subsumed by 629 during input processing: 0 [] {-} -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 0.43/0.62 Following clause subsumed by 737 during input processing: 0 [] {-} -class_Ring__and__Field_Odivision__ring(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 0.43/0.62 Following clause subsumed by 646 during input processing: 0 [flip.2] {-} -class_Ring__and__Field_Ozero__neq__one(A)|c_HOL_Ozero__class_Ozero(A)!=c_HOL_Oone__class_Oone(A).
% 0.43/0.62 Following clause subsumed by 743 during input processing: 0 [] {-} -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).
% 0.43/0.62 Following clause subsumed by 748 during input processing: 0 [] {-} -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 0.43/0.62 Following clause subsumed by 629 during input processing: 0 [] {-} -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 0.43/0.62 Following clause subsumed by 629 during input processing: 0 [] {-} -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 0.43/0.62 Following clause subsumed by 767 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 0.43/0.62 Following clause subsumed by 15 during input processing: 0 [] {-} -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C),C,A)=c_Int_Onumber__class_Onumber__of(B,A)|C=c_HOL_Ozero__class_Ozero(A).
% 0.43/0.62 Following clause subsumed by 773 during input processing: 0 [flip.4] {-} -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(C,A),A)),c_Int_Onumber__class_Onumber__of(C,A))=B|c_Int_Onumber__class_Onumber__of(C,A)=c_HOL_Ozero__class_Ozero(A).
% 0.43/0.62 Following clause subsumed by 488 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oinverse__class_Odivide(C,D,A),A)| -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A).
% 0.43/0.62 Following clause subsumed by 397 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oinverse__class_Odivide(D,C,A),A).
% 0.43/0.62 Following clause subsumed by 15 during input processing: 0 [flip.4] {-} -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C),C,A)=c_Int_Onumber__class_Onumber__of(B,A)|C=c_HOL_Ozero__class_Ozero(A).
% 0.43/0.62 Following clause subsumed by 394 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_Int_Onumber__class_Onumber__of(D,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(D,A),A)|c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A).
% 0.43/0.62 Following clause subsumed by 393 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,A),A)|c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(D,C,A),c_Int_Onumber__class_Onumber__of(B,A),A).
% 0.43/0.62 Following clause subsumed by 488 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(C,c_Int_Onumber__class_Onumber__of(D,A),A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(D,A),c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(D,A),A).
% 0.43/0.62 Following clause subsumed by 397 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(C,A),c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(C,A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(D,c_Int_Onumber__class_Onumber__of(C,A),A),A).
% 0.43/0.62 Following clause subsumed by 394 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(C,A),A),D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A)|c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(C,A),c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(C,A),A).
% 0.43/0.62 Following clause subsumed by 393 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)|c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(C,A),c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(D,c_Int_Onumber__class_Onumber__of(C,A),A),B,A).
% 0.43/0.62 Following clause subsumed by 774 during input processing: 0 [flip.5] {-} -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_Int_Onumber__class_Onumber__of(B,A)!=c_HOL_Ozero__class_Ozero(A)|c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),C),C,A)=c_Int_Onumber__class_Onumber__of(B,A).
% 0.43/0.62 Following clause subsumed by 15 during input processing: 0 [flip.4] {-} -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(C,A)),c_Int_Onumber__class_Onumber__of(C,A),A)=B|c_Int_Onumber__class_Onumber__of(C,A)=c_HOL_Ozero__class_Ozero(A).
% 0.43/0.62 Following clause subsumed by 15 during input processing: 0 [] {-} -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(C,A)),c_Int_Onumber__class_Onumber__of(C,A),A)=B|c_Int_Onumber__class_Onumber__of(C,A)=c_HOL_Ozero__class_Ozero(A).
% 0.43/0.62 Following clause subsumed by 771 during input processing: 0 [flip.4] {-} -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,A)),c_Int_Onumber__class_Onumber__of(B,A),A)=c_HOL_Ozero__class_Ozero(A).
% 0.43/0.62 Following clause subsumed by 156 during input processing: 0 [] {-} -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(A).
% 0.43/0.62 Following clause subsumed by 404 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|B=c_HOL_Ozero__class_Ozero(A)|c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),c_HOL_Ozero__class_Ozero(A),A).
% 0.43/0.62 Following clause subsumed by 403 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),c_HOL_Ozero__class_Ozero(A),A).
% 0.43/0.62 Following clause subsumed by 344 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|c_Int_Onumber__class_Onumber__of(B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat)),A)| -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat).
% 0.43/0.62 Following clause subsumed by 243 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)|c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat)|c_Int_Onumber__class_Onumber__of(C,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A).
% 0.43/0.62 Following clause subsumed by 198 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),c_HOL_Ozero__class_Ozero(A),A)| -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A)|c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat)|c_Int_Onumber__class_Onumber__of(C,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.43/0.62 Following clause subsumed by 402 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)| -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat)|c_Int_Onumber__class_Onumber__of(B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat)),c_HOL_Ozero__class_Ozero(A),A).
% 0.43/0.62 Following clause subsumed by 789 during input processing: 0 [] {-} hBOOL(hAPP(A,c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 0.43/0.62 Following clause subsumed by 790 during input processing: 0 [] {-} hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)|A=c_HOL_Ozero__class_Ozero(tc_nat)|B=C.
% 0.43/0.62 Following clause subsumed by 792 during input processing: 0 [] {-} -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 0.43/0.62 Following clause subsumed by 396 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_Int_Onumber__class_Onumber__of(D,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(D,A),A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(D,A)),C),B,A)| -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(D,A)),C),A).
% 0.43/0.62 Following clause subsumed by 806 during input processing: 0 [] {-} -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).
% 0.43/0.62 Following clause subsumed by 835 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oinverse__class_Odivide(C,D,A),A)| -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A).
% 0.43/0.62 Following clause subsumed by 836 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oinverse__class_Odivide(C,D,A),A)| -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D),C,A).
% 0.43/0.62 Following clause subsumed by 490 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oinverse__class_Odivide(C,D,A),A)| -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D),A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D),C,A).
% 0.43/0.62 Following clause subsumed by 856 during input processing: 0 [] {-} 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),D))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),B))|B=D|A=C.
% 0.43/0.62 Following clause subsumed by 857 during input processing: 0 [] {-} -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),C))|C=E|B=D.
% 0.43/0.62 Following clause subsumed by 833 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(C,A)),D),A)| -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A)| -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(C,A),c_HOL_Oinverse__class_Odivide(B,D,A),A).
% 0.43/0.62 Following clause subsumed by 834 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oinverse__class_Odivide(C,D,A),A)| -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A).
% 0.43/0.62 Following clause subsumed by 489 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oinverse__class_Odivide(C,D,A),A)| -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D),A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D),C,A).
% 0.43/0.63 Following clause subsumed by 871 during input processing: 0 [] {-} -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Oinverse__class_Odivide(B,C,A)),C)=B|C=c_HOL_Ozero__class_Ozero(A).
% 0.43/0.63 Following clause subsumed by 885 during input processing: 0 [] {-} -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 0.43/0.63 Following clause subsumed by 888 during input processing: 0 [] {-} hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.43/0.63 Following clause subsumed by 906 during input processing: 0 [] {-} A=B| -c_HOL_Oord__class_Oless(A,hAPP(c_Suc,B),tc_nat)|c_HOL_Oord__class_Oless(A,B,tc_nat).
% 0.43/0.63 Following clause subsumed by 912 during input processing: 0 [] {-} hAPP(hAPP(A,B),hAPP(c_Suc,C))=hAPP(hAPP(D,B),hAPP(hAPP(A,B),C))| -c_Groebner__Basis_Ogb__semiring(E,D,A,F,G,H).
% 0.43/0.63 Following clause subsumed by 918 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(hAPP(c_Suc,A),hAPP(c_Suc,B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 0.43/0.63 Following clause subsumed by 921 during input processing: 0 [] {-} c_lessequals(c_Int_OBit1(A),c_Int_OBit1(B),tc_Int_Oint)| -c_lessequals(A,B,tc_Int_Oint).
% 0.43/0.63 Following clause subsumed by 922 during input processing: 0 [] {-} c_lessequals(A,B,tc_Int_Oint)| -c_lessequals(c_Int_OBit1(A),c_Int_OBit1(B),tc_Int_Oint).
% 0.43/0.63 Following clause subsumed by 923 during input processing: 0 [] {-} c_lessequals(c_Int_OBit0(A),c_Int_OBit0(B),tc_Int_Oint)| -c_lessequals(A,B,tc_Int_Oint).
% 0.43/0.63 Following clause subsumed by 924 during input processing: 0 [] {-} c_lessequals(A,B,tc_Int_Oint)| -c_lessequals(c_Int_OBit0(A),c_Int_OBit0(B),tc_Int_Oint).
% 0.43/0.63 Following clause subsumed by 779 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|c_Int_Onumber__class_Onumber__of(B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat)),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A).
% 0.43/0.63 Following clause subsumed by 68 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_lessequals(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),hAPP(hAPP(c_Power_Opower__class_Opower(A),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)),A).
% 0.43/0.63 Following clause subsumed by 966 during input processing: 0 [] {-} hAPP(c_Suc,c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat))=A| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 0.43/0.63 Following clause subsumed by 297 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)| -class_Int_Onumber(A)| -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A)| -c_lessequals(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A).
% 0.43/0.63 Following clause subsumed by 295 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)| -class_Int_Onumber(A)|c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A)|c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A).
% 0.43/0.63 Following clause subsumed by 378 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)|c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat).
% 0.43/0.63 Following clause subsumed by 269 during input processing: 0 [flip.2] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),hAPP(c_Suc,C))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C)).
% 0.46/0.63 Following clause subsumed by 1000 during input processing: 0 [flip.3] {-} -class_Ring__and__Field_Ofield(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_HOL_Oinverse__class_Oinverse(C,A))=c_HOL_Oinverse__class_Odivide(B,C,A).
% 0.46/0.63 Following clause subsumed by 232 during input processing: 0 [] {-} -class_Ring__and__Field_Ofield(A)| -class_Int_Onumber(A)|c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(B,A),A)=c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),c_Int_Onumber__class_Onumber__of(B,A),A).
% 0.46/0.63 Following clause subsumed by 1007 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,C,tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),D),B),hAPP(hAPP(c_Power_Opower__class_Opower(A),D),C),A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A).
% 0.46/0.63 Following clause subsumed by 1008 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),D),A)| -c_HOL_Oord__class_Oless(C,D,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A).
% 0.46/0.63 Following clause subsumed by 603 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oinverse__class_Odivide(C,D,A),A)| -c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ozero__class_Ozero(A),A)| -c_lessequals(C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D),A)| -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),D),C,A).
% 0.46/0.63 Following clause subsumed by 604 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oinverse__class_Odivide(C,D,A),A)| -c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A).
% 0.46/0.63 Following clause subsumed by 605 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_lessequals(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oinverse__class_Odivide(D,C,A),A).
% 0.46/0.63 Following clause subsumed by 740 during input processing: 0 [] {-} -class_Ring__and__Field_Ozero__neq__one(A)| -class_Ring__and__Field_Ono__zero__divisors(A)| -class_Ring__and__Field_Omult__zero(A)| -class_Power_Opower(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat))!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 0.46/0.63 Following clause subsumed by 1096 during input processing: 0 [] {-} c_lessequals(c_Int_OBit0(A),c_Int_OBit1(B),tc_Int_Oint)| -c_lessequals(A,B,tc_Int_Oint).
% 0.46/0.63 Following clause subsumed by 1097 during input processing: 0 [] {-} c_lessequals(A,B,tc_Int_Oint)| -c_lessequals(c_Int_OBit0(A),c_Int_OBit1(B),tc_Int_Oint).
% 0.46/0.63 Following clause subsumed by 569 during input processing: 0 [] {-} hBOOL(hAPP(hAPP(A,B),C))| -hBOOL(hAPP(hAPP(D,E),C))| -hBOOL(hAPP(hAPP(A,hAPP(hAPP(c_Power_Opower_Opower(F,G,H),B),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))),hAPP(hAPP(c_Power_Opower_Opower(F,G,H),C),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))))| -c_Ring__and__Field_Oordered__semidom(I,E,F,G,D,A,H).
% 0.46/0.64 Following clause subsumed by 660 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lessequals(c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(C,A),A),D,A)| -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A)| -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),c_Int_Onumber__class_Onumber__of(C,A)),B,A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(C,A),A).
% 0.46/0.64 Following clause subsumed by 662 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lessequals(B,c_HOL_Oinverse__class_Odivide(C,c_Int_Onumber__class_Onumber__of(D,A),A),A)| -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lessequals(C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(D,A)),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(D,A),A).
% 0.46/0.64 Following clause subsumed by 1140 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 0.46/0.64 Following clause subsumed by 1139 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 0.46/0.64 Following clause subsumed by 661 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),c_Int_Onumber__class_Onumber__of(D,A),A)| -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(D,A),A)|c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lessequals(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(D,A)),C),A).
% 0.46/0.64 Following clause subsumed by 660 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lessequals(c_HOL_Oinverse__class_Odivide(B,C,A),c_Int_Onumber__class_Onumber__of(D,A),A)| -c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(D,A),A)| -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(D,A)),C),B,A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A).
% 0.46/0.64 Following clause subsumed by 606 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lessequals(c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(C,A),A),D,A)| -c_lessequals(c_HOL_Ozero__class_Ozero(A),D,A)| -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),c_Int_Onumber__class_Onumber__of(C,A)),B,A)| -c_lessequals(B,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),c_Int_Onumber__class_Onumber__of(C,A)),A).
% 0.46/0.64 Following clause subsumed by 603 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)| -class_Int_Onumber(A)|c_lessequals(B,c_HOL_Oinverse__class_Odivide(C,c_Int_Onumber__class_Onumber__of(D,A),A),A)| -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A)| -c_lessequals(C,hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(D,A)),A)| -c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Int_Onumber__class_Onumber__of(D,A)),C,A).
% 0.46/0.64 Following clause subsumed by 657 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat)),A)|B=c_HOL_Ozero__class_Ozero(A)| -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat).
% 0.46/0.64 Following clause subsumed by 712 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A)| -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A)|c_Parity_Oeven__odd__class_Oeven(C,tc_nat).
% 0.46/0.64 Following clause subsumed by 1186 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A)| -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A)|c_Parity_Oeven__odd__class_Oeven(C,tc_nat).
% 0.46/0.64 Following clause subsumed by 712 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A)| -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A)|c_Parity_Oeven__odd__class_Oeven(C,tc_nat).
% 0.46/0.64 Following clause subsumed by 1186 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A)|c_Parity_Oeven__odd__class_Oeven(C,tc_nat)| -c_lessequals(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_Power_Opower__class_Opower(A),B),C),A).
% 0.46/0.64 Following clause subsumed by 445 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Oabs__class_Oabs(B,A)),c_Int_Onumber__class_Onumber__of(C,tc_nat))=hAPP(hAPP(c_Power_Opower__class_Opower(A),B),c_Int_Onumber__class_Onumber__of(C,tc_nat))| -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat).
% 0.46/0.64 Following clause subsumed by 848 during input processing: 0 [] {-} -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Odivide(hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_HOL_Ozero__class_Ozero(A)),B),B,A)=c_HOL_Ozero__class_Ozero(A).
% 0.46/0.64 Following clause subsumed by 308 during input processing: 0 [flip.1] {-} hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)!=c_HOL_Oone__class_Oone(tc_nat)|B=c_HOL_Oone__class_Oone(tc_nat).
% 0.46/0.64 Following clause subsumed by 307 during input processing: 0 [flip.1] {-} hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)!=c_HOL_Oone__class_Oone(tc_nat)|A=c_HOL_Oone__class_Oone(tc_nat).
% 0.46/0.64 Following clause subsumed by 1203 during input processing: 0 [] {-} -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 0.46/0.64 Following clause subsumed by 1116 during input processing: 0 [] {-} -class_OrderedGroup_Omonoid__mult(A)| -class_Int_Onumber(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_Int_Onumber__class_Onumber__of(B,A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat))=hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Int_Onumber__class_Onumber__of(B,A)),c_Int_Onumber__class_Onumber__of(B,A)).
% 0.46/0.64 Following clause subsumed by 1065 during input processing: 0 [] {-} -class_Ring__and__Field_Ozero__neq__one(A)| -class_Ring__and__Field_Ono__zero__divisors(A)| -class_Ring__and__Field_Omult__zero(A)| -class_Power_Opower(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat))=c_HOL_Ozero__class_Ozero(A)|c_Int_Onumber__class_Onumber__of(B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.46/0.64 Following clause subsumed by 1064 during input processing: 0 [] {-} -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|hAPP(hAPP(c_Power_Opower__class_Opower(A),c_HOL_Ozero__class_Ozero(A)),c_Int_Onumber__class_Onumber__of(B,tc_nat))=c_HOL_Ozero__class_Ozero(A)|c_Int_Onumber__class_Onumber__of(B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.46/0.64 Following clause subsumed by 1243 during input processing: 0 [] {-} -class_Ring__and__Field_Ofield(A)| -class_Int_Onumber__ring(A)|c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),A),A)=B.
% 0.46/0.64 Following clause subsumed by 1260 during input processing: 0 [] {-} hAPP(c_Suc,A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.46/0.64 Following clause subsumed by 1259 during input processing: 0 [flip.2] {-} -class_Int_Onumber__ring(A)|c_HOL_Ozero__class_Ozero(A)=c_Int_Onumber__class_Onumber__of(c_Int_OPls,A).
% 0.46/0.64 Following clause subsumed by 1261 during input processing: 0 [] {-} hAPP(c_Suc,A)!=hAPP(c_Suc,B)|A=B.
% 0.46/0.64 Following clause subsumed by 1263 during input processing: 0 [] {-} c_Int_OBit1(A)!=c_Int_OPls.
% 0.46/0.68 Following clause subsumed by 1267 during input processing: 0 [flip.1] {-} hAPP(c_Suc,A)!=A.
% 0.46/0.68 Following clause subsumed by 1270 during input processing: 0 [] {-} c_HOL_Ozero__class_Ozero(tc_nat)!=hAPP(c_Suc,A).
% 0.46/0.68 15 back subsumes 13.
% 0.46/0.68 204 back subsumes 201.
% 0.46/0.68 205 back subsumes 203.
% 0.46/0.68 297 back subsumes 296.
% 0.46/0.68 349 back subsumes 38.
% 0.46/0.68 350 back subsumes 37.
% 0.46/0.68 395 back subsumes 267.
% 0.46/0.68 395 back subsumes 240.
% 0.46/0.68 396 back subsumes 239.
% 0.46/0.68 460 back subsumes 98.
% 0.46/0.68 489 back subsumes 266.
% 0.46/0.68 490 back subsumes 238.
% 0.46/0.68 542 back subsumes 539.
% 0.46/0.68 543 back subsumes 540.
% 0.46/0.68 604 back subsumes 162.
% 0.46/0.68 605 back subsumes 161.
% 0.46/0.68 606 back subsumes 150.
% 0.46/0.68 607 back subsumes 160.
% 0.46/0.68 607 back subsumes 151.
% 0.46/0.68 608 back subsumes 159.
% 0.46/0.68 608 back subsumes 152.
% 0.46/0.68 661 back subsumes 345.
% 0.46/0.68 662 back subsumes 227.
% 0.46/0.68 663 back subsumes 346.
% 0.46/0.68 663 back subsumes 226.
% 0.46/0.68 712 back subsumes 104.
% 0.46/0.68 792 back subsumes 787.
% 0.46/0.68 808 back subsumes 174.
% 0.46/0.68 829 back subsumes 667.
% 0.46/0.68 829 back subsumes 235.
% 0.46/0.68 830 back subsumes 668.
% 0.46/0.68 830 back subsumes 234.
% 0.46/0.68 831 back subsumes 803.
% 0.46/0.68 831 back subsumes 801.
% 0.46/0.68 832 back subsumes 802.
% 0.46/0.68 832 back subsumes 263.
% 0.46/0.68 833 back subsumes 669.
% 0.46/0.68 834 back subsumes 670.
% 0.46/0.68 835 back subsumes 804.
% 0.46/0.68 836 back subsumes 262.
% 0.46/0.68 848 back subsumes 771.
% 0.46/0.68 871 back subsumes 773.
% 0.46/0.68 960 back subsumes 959.
% 0.46/0.68 966 back subsumes 905.
% 0.46/0.68 983 back subsumes 446.
% 0.46/0.68 1021 back subsumes 732.
% 0.46/0.68 1021 back subsumes 278.
% 0.46/0.68 1022 back subsumes 733.
% 0.46/0.68 1022 back subsumes 279.
% 0.46/0.68 1023 back subsumes 868.
% 0.46/0.68 1023 back subsumes 734.
% 0.46/0.68 1024 back subsumes 867.
% 0.46/0.68 1024 back subsumes 735.
% 0.46/0.68 1186 back subsumes 105.
% 0.46/0.68 Following clause subsumed by 1270 during input processing: 0 [copy,1260,flip.1] {-} c_HOL_Ozero__class_Ozero(tc_nat)!=hAPP(c_Suc,A).
% 0.46/0.68 Following clause subsumed by 1273 during input processing: 0 [copy,1266,flip.1] {-} c_Int_OBit0(A)!=c_Int_OBit1(B).
% 0.46/0.68 Following clause subsumed by 1260 during input processing: 0 [copy,1270,flip.1] {-} hAPP(c_Suc,A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.46/0.68 Following clause subsumed by 1266 during input processing: 0 [copy,1273,flip.1] {-} c_Int_OBit1(A)!=c_Int_OBit0(B).
% 0.46/0.68 1344 back subsumes 1343.
% 0.46/0.68
% 0.46/0.68 ------------> process sos:
% 0.46/0.68 Following clause subsumed by 1501 during input processing: 0 [] {-} hBOOL(hAPP(hAPP(A,B),C))|c_HOL_Oord__class_Oless(B,C,tc_nat)|C=B|c_HOL_Oord__class_Oless(C,B,tc_nat).
% 0.46/0.68 Following clause subsumed by 1501 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 0.46/0.68 Following clause subsumed by 1515 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(A,hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),tc_nat).
% 0.46/0.68 Following clause subsumed by 1540 during input processing: 0 [] {-} 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))=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),A),B)).
% 0.46/0.68 Following clause subsumed by 1568 during input processing: 0 [] {-} c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat)|c_Parity_Oeven__odd__class_Oeven(B,tc_nat)|c_Parity_Oeven__odd__class_Oeven(A,tc_nat).
% 0.46/0.68 Following clause subsumed by 1568 during input processing: 0 [] {-} c_Parity_Oeven__odd__class_Oeven(A,tc_nat)|c_Parity_Oeven__odd__class_Oeven(B,tc_nat)|c_Parity_Oeven__odd__class_Oeven(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat).
% 0.46/0.68 Following clause subsumed by 1603 during input processing: 0 [demod,1600,1600] {-} c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.46/0.68 Following clause subsumed by 1627 during input processing: 0 [demod,1644,1642] {-} hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))=hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)).
% 0.46/0.68 Following clause subsumed by 1649 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(A,hAPP(c_Suc,A),tc_nat).
% 0.46/0.68 Following clause subsumed by 1649 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(A,hAPP(c_Suc,A),tc_nat).
% 0.46/0.68 Following clause subsumed by 1627 during input processing: 0 [demod,1509,1529] {-} c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat).
% 0.46/0.68 Following clause subsumed by 1627 during input processing: 0 [demod,1509,1529] {-} c_Int_Onumber__class_Onumber__of(A,tc_nat)=c_Int_Onumber__class_Onumber__of(A,tc_nat).
% 0.46/0.68 Following clause subsumed by 1627 during input processing: 0 [demod,1642,1625] {-} hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)).
% 0.46/0.68 Following clause subsumed by 1627 during input processing: 0 [demod,1625] {-} hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)).
% 0.46/0.68 Following clause subsumed by 1627 during input processing: 0 [demod,1506,1600,1625] {-} hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)).
% 0.46/0.68 Following clause subsumed by 1649 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 0.46/0.68 Following clause subsumed by 1627 during input processing: 0 [demod,1661,1661,1539,1661] {-} c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 0.46/0.68 Following clause subsumed by 1627 during input processing: 0 [demod,1661,1625,1661] {-} c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 0.46/0.68 Following clause subsumed by 1665 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,A),tc_nat).
% 0.46/0.68 Following clause subsumed by 1627 during input processing: 0 [demod,1509,1529] {-} c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat).
% 0.46/0.68 Following clause subsumed by 1627 during input processing: 0 [demod,1689,1506,1533] {-} hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),A).
% 0.46/0.68 Following clause subsumed by 1627 during input processing: 0 [demod,1509,1529,1689,1661] {-} hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat))=hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)).
% 0.46/0.68 Following clause subsumed by 1627 during input processing: 0 [demod,1713] {-} c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 0.46/0.68 Following clause subsumed by 1665 during input processing: 0 [demod,1689] {-} c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_Suc,c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 0.46/0.68 Following clause subsumed by 1627 during input processing: 0 [demod,1689,1644,1536] {-} hAPP(c_Suc,hAPP(c_Suc,A))=hAPP(c_Suc,hAPP(c_Suc,A)).
% 0.46/0.68 Following clause subsumed by 1627 during input processing: 0 [demod,1689,1642,1539] {-} hAPP(c_Suc,hAPP(c_Suc,A))=hAPP(c_Suc,hAPP(c_Suc,A)).
% 0.46/0.68 Following clause subsumed by 1627 during input processing: 0 [demod,1723] {-} c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat).
% 0.46/0.68 Following clause subsumed by 1627 during input processing: 0 [demod,1728] {-} c_Int_OPls=c_Int_OPls.
% 0.46/0.68 Following clause subsumed by 1627 during input processing: 0 [demod,1723,1689,1731] {-} hAPP(c_Suc,hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)))=hAPP(c_Suc,hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat))).
% 0.46/0.68 Following clause subsumed by 1627 during input processing: 0 [] {-} A=A.
% 0.46/0.68 Following clause subsumed by 1541 during input processing: 0 [copy,1541,flip.1] {-} hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A).
% 0.46/0.68 Following clause subsumed by 1544 during input processing: 0 [copy,1544,flip.1] {-} 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)).
% 0.46/0.68 Following clause subsumed by 1570 during input processing: 0 [copy,1557,flip.1] {-} c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))=c_Set_Oimage(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C,A).
% 0.52/0.70 Following clause subsumed by 1566 during input processing: 0 [copy,1566,flip.1] {-} c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,C,tc_nat),B,tc_nat).
% 0.52/0.70 Following clause subsumed by 1557 during input processing: 0 [copy,1570,flip.1] {-} c_Set_Oimage(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B,C)=c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)).
% 0.52/0.70 Following clause subsumed by 1627 during input processing: 0 [copy,1572,flip.1,demod,1731,1731] {-} hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat))=hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)).
% 0.52/0.70 Following clause subsumed by 1627 during input processing: 0 [copy,1603,flip.1,demod,1723,1723] {-} c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat).
% 0.52/0.70 Following clause subsumed by 1608 during input processing: 0 [copy,1608,flip.1] {-} hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).
% 0.52/0.70 Following clause subsumed by 1627 during input processing: 0 [copy,1627,flip.1] {-} A=A.
% 0.52/0.70 1627 back subsumes 1603.
% 0.52/0.70 1627 back subsumes 1572.
% 0.52/0.70 1627 back subsumes 1492.
% 0.52/0.70 1627 back subsumes 1491.
% 0.52/0.70 1627 back subsumes 1417.
% 0.52/0.70 1627 back subsumes 1414.
% 0.52/0.70 1627 back subsumes 1411.
% 0.52/0.70 1627 back subsumes 1410.
% 0.52/0.70 1627 back subsumes 1409.
% 0.52/0.70 1627 back subsumes 1382.
% 0.52/0.70 1627 back subsumes 1366.
% 0.52/0.70 1627 back subsumes 1332.
% 0.52/0.70 1627 back subsumes 1331.
% 0.52/0.70 1627 back subsumes 1287.
% 0.52/0.70 1627 back subsumes 1283.
% 0.52/0.70 1627 back subsumes 1282.
% 0.52/0.70 1627 back subsumes 1281.
% 0.52/0.70 1627 back subsumes 1280.
% 0.52/0.70 1692 back subsumes 1653.
% 0.52/0.70 Following clause subsumed by 1507 during input processing: 0 [copy,1832,flip.1] {-} hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,A)),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)).
% 0.52/0.70 Following clause subsumed by 1837 during input processing: 0 [copy,1837,flip.1] {-} 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_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B)).
% 0.52/0.70 Following clause subsumed by 1546 during input processing: 0 [copy,1840,flip.1] {-} c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat).
% 0.52/0.70 Following clause subsumed by 1552 during input processing: 0 [copy,1841,flip.1] {-} 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)).
% 0.52/0.70 Following clause subsumed by 2113 during input processing: 0 [copy,1844,flip.1] {-} c_HOL_Ominus__class_Ominus(A,hAPP(c_Suc,B),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)),tc_nat),B,tc_nat).
% 0.52/0.70 Following clause subsumed by 2013 during input processing: 0 [copy,1860,flip.1] {-} c_HOL_Ominus__class_Ominus(A,A,tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat).
% 0.52/0.70 Following clause subsumed by 1656 during input processing: 0 [copy,1875,flip.1] {-} c_Divides_Odiv__class_Odiv(A,hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C),tc_nat)=c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(A,B,tc_nat),C,tc_nat).
% 0.52/0.70 Following clause subsumed by 2106 during input processing: 0 [copy,1982,flip.1] {-} hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)))),A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),A).
% 0.52/0.70 Following clause subsumed by 2002 during input processing: 0 [copy,1983,flip.1,demod,1985] {-} c_SetInterval_Oord__class_OatLeastLessThan(A,c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),tc_nat)=c_SetInterval_Oord__class_OatLeastLessThan(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),tc_nat).
% 0.52/0.70 1986 back subsumes 1177.
% 0.52/0.71 Following clause subsumed by 1704 during input processing: 0 [copy,1988,flip.1] {-} c_Set_Oimage(c_Suc,c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat),tc_nat,tc_nat)=c_SetInterval_Oord__class_OatLeastAtMost(hAPP(c_Suc,A),B,tc_nat).
% 0.52/0.71 Following clause subsumed by 1705 during input processing: 0 [copy,1989,flip.1] {-} c_SetInterval_Oord__class_OatLeastLessThan(hAPP(c_Suc,A),B,tc_nat)=c_SetInterval_Oord__class_OgreaterThanLessThan(A,B,tc_nat).
% 0.52/0.71 Following clause subsumed by 2105 during input processing: 0 [copy,1999,flip.1] {-} c_Divides_Odiv__class_Odiv(hAPP(c_Suc,hAPP(c_Suc,A)),hAPP(c_Suc,hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat))),tc_nat)=hAPP(c_Suc,c_Divides_Odiv__class_Odiv(A,hAPP(c_Suc,hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat))),tc_nat)).
% 0.52/0.71 Following clause subsumed by 2126 during input processing: 0 [copy,2002,flip.1] {-} c_SetInterval_Oord__class_OatLeastLessThan(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),tc_nat)=c_SetInterval_Oord__class_OatLeastLessThan(A,c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),tc_nat).
% 0.52/0.71 Following clause subsumed by 1860 during input processing: 0 [copy,2013,flip.1] {-} c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)=c_HOL_Ominus__class_Ominus(A,A,tc_nat).
% 0.52/0.71 Following clause subsumed by 1999 during input processing: 0 [copy,2105,flip.1] {-} hAPP(c_Suc,c_Divides_Odiv__class_Odiv(A,hAPP(c_Suc,hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat))),tc_nat))=c_Divides_Odiv__class_Odiv(hAPP(c_Suc,hAPP(c_Suc,A)),hAPP(c_Suc,hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat))),tc_nat).
% 0.52/0.71 Following clause subsumed by 1982 during input processing: 0 [copy,2106,flip.1] {-} hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),A)=hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(c_Suc,hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)))),A).
% 0.52/0.71 Following clause subsumed by 1844 during input processing: 0 [copy,2113,flip.1] {-} c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,hAPP(c_Suc,c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)),tc_nat),B,tc_nat)=c_HOL_Ominus__class_Ominus(A,hAPP(c_Suc,B),tc_nat).
% 0.52/0.71 Following clause subsumed by 2002 during input processing: 0 [copy,2126,flip.1] {-} c_SetInterval_Oord__class_OatLeastLessThan(A,c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),tc_nat)=c_SetInterval_Oord__class_OatLeastLessThan(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),tc_nat).
% 0.52/0.71
% 0.52/0.71 ======= end of input processing =======
% 0.52/0.74
% 0.52/0.74 Input error on line 30: function p_c_Ring__and__Field_Oordered__idom: thing, thing, thing, thing, thing, thing, thing, thing, thing, thing, thing -> bool {no_priority}
% 0.52/0.74
% 0.52/0.74
% 0.52/0.74 Adicity too great for function p_c_Ring__and__Field_Oordered__idom
% 0.52/0.74
%------------------------------------------------------------------------------