TSTP Solution File: SWV632-1 by SOS---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SOS---2.0
% Problem : SWV632-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : sos-script %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 21:39:43 EDT 2022
% Result : Unknown 0.60s 0.85s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV632-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : sos-script %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 15 08:07:02 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.53 ----- Otter 3.2, August 2001 -----
% 0.20/0.53 The process was started by sandbox2 on n016.cluster.edu,
% 0.20/0.53 Wed Jun 15 08:07:02 2022
% 0.20/0.53 The command was "./sos". The process ID is 20569.
% 0.20/0.53
% 0.20/0.53 set(prolog_style_variables).
% 0.20/0.53 set(auto).
% 0.20/0.53 dependent: set(auto1).
% 0.20/0.53 dependent: set(process_input).
% 0.20/0.53 dependent: clear(print_kept).
% 0.20/0.53 dependent: clear(print_new_demod).
% 0.20/0.53 dependent: clear(print_back_demod).
% 0.20/0.53 dependent: clear(print_back_sub).
% 0.20/0.53 dependent: set(control_memory).
% 0.20/0.53 dependent: assign(max_mem, 12000).
% 0.20/0.53 dependent: assign(pick_given_ratio, 4).
% 0.20/0.53 dependent: assign(stats_level, 1).
% 0.20/0.53 dependent: assign(pick_semantic_ratio, 3).
% 0.20/0.53 dependent: assign(sos_limit, 5000).
% 0.20/0.53 dependent: assign(max_weight, 60).
% 0.20/0.53 clear(print_given).
% 0.20/0.53
% 0.20/0.53 list(usable).
% 0.20/0.53
% 0.20/0.53 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 0.20/0.53
% 0.20/0.53 This ia a non-Horn set with equality. The strategy will be
% 0.20/0.53 Knuth-Bendix, ordered hyper_res, ur_res, factoring, and
% 0.20/0.53 unit deletion, with positive clauses in sos and nonpositive
% 0.20/0.53 clauses in usable.
% 0.20/0.53
% 0.20/0.53 dependent: set(knuth_bendix).
% 0.20/0.53 dependent: set(para_from).
% 0.20/0.53 dependent: set(para_into).
% 0.20/0.53 dependent: clear(para_from_right).
% 0.20/0.53 dependent: clear(para_into_right).
% 0.20/0.53 dependent: set(para_from_vars).
% 0.20/0.53 dependent: set(eq_units_both_ways).
% 0.20/0.53 dependent: set(dynamic_demod_all).
% 0.20/0.53 dependent: set(dynamic_demod).
% 0.20/0.53 dependent: set(order_eq).
% 0.20/0.53 dependent: set(back_demod).
% 0.20/0.53 dependent: set(lrpo).
% 0.20/0.53 dependent: set(hyper_res).
% 0.20/0.53 dependent: set(unit_deletion).
% 0.20/0.53 dependent: set(factor).
% 0.20/0.53
% 0.20/0.53 ------------> process usable:
% 0.20/0.53 Following clause subsumed by 52 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).
% 0.20/0.53 Following clause subsumed by 52 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).
% 0.20/0.53 Following clause subsumed by 54 during input processing: 0 [] {-} A=B| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 0.20/0.53 Following clause subsumed by 54 during input processing: 0 [] {-} -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)|B=A| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat).
% 0.20/0.53 Following clause subsumed by 54 during input processing: 0 [] {-} A=B| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 0.20/0.53 Following clause subsumed by 54 during input processing: 0 [] {-} A=B| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat).
% 0.20/0.53 Following clause subsumed by 54 during input processing: 0 [] {-} -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)|B=A| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat).
% 0.20/0.53 Following clause subsumed by 54 during input processing: 0 [] {-} -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat)|B=A.
% 0.20/0.53 Following clause subsumed by 53 during input processing: 0 [] {-} -class_Orderings_Oorder(A)|B=C| -c_lessequals(C,B,A)| -c_lessequals(B,C,A).
% 0.20/0.53 Following clause subsumed by 52 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A)|C=B.
% 0.20/0.53 Following clause subsumed by 53 during input processing: 0 [] {-} -class_Orderings_Oorder(A)|B=C| -c_lessequals(C,B,A)| -c_lessequals(B,C,A).
% 0.20/0.53 Following clause subsumed by 58 during input processing: 0 [] {-} -class_Ring__and__Field_Ofield(A)|B=c_HOL_Ozero__class_Ozero(A)|c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(C,B,A),B,A)=C.
% 0.20/0.53 Following clause subsumed by 58 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(c_HOL_Otimes__class_Otimes(B,C,A),C,A)=B|C=c_HOL_Ozero__class_Ozero(A).
% 0.20/0.53 Following clause subsumed by 58 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_Otimes__class_Otimes(B,C,A),C,A)=B|C=c_HOL_Ozero__class_Ozero(A).
% 0.20/0.53 Following clause subsumed by 109 during input processing: 0 [] {-} -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 0.20/0.53 Following clause subsumed by 123 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(c_HOL_Otimes__class_Otimes(B,D,A),C,A).
% 0.20/0.53 Following clause subsumed by 124 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,c_HOL_Otimes__class_Otimes(D,C,A),A).
% 0.20/0.53 Following clause subsumed by 131 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),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).
% 0.20/0.53 Following clause subsumed by 151 during input processing: 0 [] {-} c_Suc(A)!=A.
% 0.20/0.53 Following clause subsumed by 158 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_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),C,A),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).
% 0.20/0.53 Following clause subsumed by 161 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(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),D,A),C,A).
% 0.20/0.53 Following clause subsumed by 123 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(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),D,A),C,A).
% 0.20/0.53 Following clause subsumed by 125 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_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),C,A),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).
% 0.20/0.53 Following clause subsumed by 198 during input processing: 0 [] {-} -class_Divides_Osemiring__div(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A),c_Divides_Odiv__class_Omod(B,C,A),A)=B.
% 0.20/0.53 Following clause subsumed by 200 during input processing: 0 [] {-} -class_Orderings_Oorder(A)|B=C|c_HOL_Oord__class_Oless(B,C,A)| -c_lessequals(B,C,A).
% 0.20/0.53 Following clause subsumed by 200 during input processing: 0 [] {-} -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)|B=C| -c_lessequals(B,C,A).
% 0.20/0.53 Following clause subsumed by 200 during input processing: 0 [] {-} -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_lessequals(B,C,A)|B=C.
% 0.20/0.53 Following clause subsumed by 201 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(B,C,A)| -c_lessequals(B,C,A).
% 0.20/0.53 Following clause subsumed by 202 during input processing: 0 [] {-} -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)|C=B| -c_lessequals(B,C,A).
% 0.20/0.54 Following clause subsumed by 208 during input processing: 0 [] {-} -class_Ring__and__Field_Opordered__ring(A)|c_lessequals(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A)| -c_lessequals(C,c_HOL_Ozero__class_Ozero(A),A)| -c_lessequals(B,c_HOL_Ozero__class_Ozero(A),A).
% 0.20/0.54 Following clause subsumed by 130 during input processing: 0 [] {-} c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.20/0.54 Following clause subsumed by 225 during input processing: 0 [] {-} c_Nat_Osemiring__1__class_Oof__nat(A,tc_Int_Oint)!=c_Nat_Osemiring__1__class_Oof__nat(B,tc_Int_Oint)|A=B.
% 0.20/0.54 Following clause subsumed by 26 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A),A).
% 0.20/0.54 Following clause subsumed by 77 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,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),D,A),A)| -c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),D,A),C,A).
% 0.20/0.54 Following clause subsumed by 234 during input processing: 0 [] {-} -class_Divides_Osemiring__div(A)|c_Ring__and__Field_Odvd__class_Odvd(B,C,A)| -c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A).
% 0.20/0.54 Following clause subsumed by 235 during input processing: 0 [] {-} -class_Divides_Osemiring__div(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,A).
% 0.20/0.54 Following clause subsumed by 242 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 0.20/0.54 Following clause subsumed by 243 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 0.20/0.54 Following clause subsumed by 252 during input processing: 0 [flip.1] {-} c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.20/0.54 Following clause subsumed by 261 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).
% 0.20/0.54 Following clause subsumed by 154 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),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).
% 0.20/0.54 Following clause subsumed by 305 during input processing: 0 [flip.2] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A).
% 0.20/0.54 Following clause subsumed by 243 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 0.20/0.54 Following clause subsumed by 242 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 0.20/0.54 Following clause subsumed by 124 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,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(D,A),C,A),A).
% 0.20/0.54 Following clause subsumed by 126 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_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(C,A),D,A),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).
% 0.20/0.54 Following clause subsumed by 261 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).
% 0.20/0.54 Following clause subsumed by 349 during input processing: 0 [] {-} c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(B,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(A,tc_nat).
% 0.20/0.54 Following clause subsumed by 351 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(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat).
% 0.20/0.54 Following clause subsumed by 350 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(c_HOL_Oplus__class_Oplus(B,A,tc_nat),tc_nat).
% 0.20/0.54 Following clause subsumed by 350 during input processing: 0 [] {-} -c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)|c_Parity_Oeven__odd__class_Oeven(B,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(A,tc_nat).
% 0.20/0.54 Following clause subsumed by 351 during input processing: 0 [] {-} -c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(B,tc_nat)|c_Parity_Oeven__odd__class_Oeven(A,tc_nat).
% 0.20/0.54 Following clause subsumed by 349 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(c_HOL_Oplus__class_Oplus(B,A,tc_nat),tc_nat).
% 0.20/0.54 Following clause subsumed by 359 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).
% 0.20/0.54 Following clause subsumed by 358 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).
% 0.20/0.54 Following clause subsumed by 376 during input processing: 0 [flip.2] {-} -class_OrderedGroup_Oab__group__add(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Ouminus__class_Ouminus(C,A),A)=c_HOL_Ominus__class_Ominus(B,C,A).
% 0.20/0.54 Following clause subsumed by 305 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A).
% 0.20/0.54 Following clause subsumed by 401 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,B,A)|c_lessequals(B,B,A).
% 0.20/0.54 Following clause subsumed by 401 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_lessequals(B,C,A)|c_HOL_Oord__class_Oless(C,B,A).
% 0.20/0.54 Following clause subsumed by 401 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_lessequals(C,B,A).
% 0.20/0.54 Following clause subsumed by 403 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)| -c_lessequals(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 0.20/0.54 Following clause subsumed by 404 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).
% 0.20/0.54 Following clause subsumed by 404 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).
% 0.20/0.54 Following clause subsumed by 191 during input processing: 0 [flip.2] {-} -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Omod(C,D,A),A),D,A)=c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),D,A).
% 0.20/0.54 Following clause subsumed by 192 during input processing: 0 [flip.2] {-} -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,D,A),C,A),D,A)=c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),D,A).
% 0.20/0.54 Following clause subsumed by 432 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A)| -c_Parity_Oeven__odd__class_Oeven(C,tc_nat).
% 0.20/0.54 Following clause subsumed by 437 during input processing: 0 [] {-} -class_OrderedGroup_Ogroup__add(A)|c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(B,A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 0.20/0.54 Following clause subsumed by 452 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).
% 0.20/0.54 Following clause subsumed by 153 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|c_lessequals(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),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).
% 0.20/0.54 Following clause subsumed by 161 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(c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(D,A),A),C,A).
% 0.20/0.54 Following clause subsumed by 158 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_Otimes__class_Otimes(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,c_HOL_Oinverse__class_Odivide(D,c_Int_Onumber__class_Onumber__of(C,A),A),A).
% 0.20/0.54 Following clause subsumed by 160 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,c_HOL_Otimes__class_Otimes(D,c_Int_Onumber__class_Onumber__of(C,A),A),A).
% 0.20/0.54 Following clause subsumed by 156 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_Otimes__class_Otimes(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(c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(D,A),A),C,A).
% 0.20/0.54 Following clause subsumed by 471 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).
% 0.20/0.54 Following clause subsumed by 452 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).
% 0.20/0.54 Following clause subsumed by 479 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).
% 0.20/0.54 Following clause subsumed by 482 during input processing: 0 [] {-} c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=c_HOL_Oplus__class_Oplus(A,C,tc_nat)|B=C.
% 0.20/0.54 Following clause subsumed by 491 during input processing: 0 [] {-} -class_Ring__and__Field_Opordered__cancel__semiring(A)|c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),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).
% 0.20/0.54 Following clause subsumed by 492 during input processing: 0 [] {-} -class_Ring__and__Field_Opordered__cancel__semiring(A)|c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),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).
% 0.20/0.54 Following clause subsumed by 492 during input processing: 0 [] {-} -class_Ring__and__Field_Opordered__cancel__semiring(A)|c_lessequals(c_HOL_Otimes__class_Otimes(B,C,A),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).
% 0.20/0.54 Following clause subsumed by 156 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_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(C,A),D,A),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).
% 0.20/0.54 Following clause subsumed by 160 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,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(D,A),C,A),A).
% 0.20/0.54 Following clause subsumed by 78 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(c_HOL_Otimes__class_Otimes(D,c_Int_Onumber__class_Onumber__of(C,A),A),B,A)| -c_lessequals(B,c_HOL_Otimes__class_Otimes(D,c_Int_Onumber__class_Onumber__of(C,A),A),A).
% 0.20/0.54 Following clause subsumed by 77 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,c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(D,A),A),A)| -c_lessequals(c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(D,A),A),C,A).
% 0.20/0.54 Following clause subsumed by 81 during input processing: 0 [] {-} -class_Ring__and__Field_Ozero__neq__one(A)|c_HOL_Ozero__class_Ozero(A)!=c_HOL_Oone__class_Oone(A).
% 0.20/0.54 Following clause subsumed by 49 during input processing: 0 [] {-} -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat).
% 0.20/0.54 Following clause subsumed by 341 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).
% 0.20/0.54 Following clause subsumed by 342 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).
% 0.20/0.54 Following clause subsumed by 345 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).
% 0.20/0.54 Following clause subsumed by 346 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).
% 0.20/0.54 Following clause subsumed by 432 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),A)| -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat).
% 0.20/0.54 Following clause subsumed by 528 during input processing: 0 [] {-} -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 0.20/0.54 Following clause subsumed by 27 during input processing: 0 [] {-} -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Oone__class_Oone(A).
% 0.20/0.54 Following clause subsumed by 173 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(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),c_HOL_Ozero__class_Ozero(A),A).
% 0.20/0.54 Following clause subsumed by 123 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(c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(D,A),A),C,A).
% 0.20/0.54 Following clause subsumed by 125 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_Otimes__class_Otimes(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,c_HOL_Oinverse__class_Odivide(D,c_Int_Onumber__class_Onumber__of(C,A),A),A).
% 0.20/0.55 Following clause subsumed by 124 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,c_HOL_Otimes__class_Otimes(D,c_Int_Onumber__class_Onumber__of(C,A),A),A).
% 0.20/0.55 Following clause subsumed by 126 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_Otimes__class_Otimes(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(c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(D,A),A),C,A).
% 0.20/0.55 Following clause subsumed by 573 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(D,B,A).
% 0.20/0.55 Following clause subsumed by 576 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(D,C,A).
% 0.20/0.55 Following clause subsumed by 577 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(C,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 0.20/0.55 Following clause subsumed by 576 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(D,C,A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 0.20/0.55 Following clause subsumed by 581 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),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).
% 0.20/0.55 Following clause subsumed by 581 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),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).
% 0.20/0.55 Following clause subsumed by 583 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),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).
% 0.20/0.55 Following clause subsumed by 417 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(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A),c_HOL_Ozero__class_Ozero(A),A).
% 0.20/0.55 Following clause subsumed by 590 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__semidom(A)|c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A).
% 0.20/0.55 Following clause subsumed by 596 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A)=B.
% 0.20/0.55 Following clause subsumed by 612 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.
% 0.20/0.55 Following clause subsumed by 612 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.
% 0.20/0.55 Following clause subsumed by 612 during input processing: 0 [] {-} -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A)=B.
% 0.20/0.55 Following clause subsumed by 618 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 0.20/0.55 Following clause subsumed by 620 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).
% 0.20/0.55 Following clause subsumed by 621 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).
% 0.20/0.55 Following clause subsumed by 622 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).
% 0.20/0.55 Following clause subsumed by 623 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).
% 0.20/0.55 Following clause subsumed by 49 during input processing: 0 [] {-} -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat).
% 0.20/0.55 Following clause subsumed by 49 during input processing: 0 [] {-} -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat).
% 0.20/0.55 Following clause subsumed by 250 during input processing: 0 [flip.2] {-} -class_Ring__and__Field_Oring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,A),C,A),D,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A).
% 0.20/0.55 Following clause subsumed by 78 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(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(D,A),C,A),B,A)| -c_lessequals(B,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(D,A),C,A),A).
% 0.20/0.55 Following clause subsumed by 434 during input processing: 0 [flip.2] {-} -class_Int_Onumber__ring(A)|c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(A),A)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,A).
% 0.20/0.55 Following clause subsumed by 341 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).
% 0.20/0.55 Following clause subsumed by 342 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).
% 0.20/0.55 Following clause subsumed by 344 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_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(D,A),C,A),B,A)| -c_HOL_Oord__class_Oless(B,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(D,A),C,A),A).
% 0.20/0.55 Following clause subsumed by 659 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(B,C,A)=c_HOL_Oplus__class_Oplus(C,B,A).
% 0.20/0.55 Following clause subsumed by 686 during input processing: 0 [] {-} c_Suc(A)!=c_Suc(B)|A=B.
% 0.20/0.55 Following clause subsumed by 681 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,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),D,A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A).
% 0.20/0.55 Following clause subsumed by 682 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_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),D,A),C,A).
% 0.20/0.55 Following clause subsumed by 345 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).
% 0.20/0.55 Following clause subsumed by 346 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).
% 0.20/0.55 Following clause subsumed by 348 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,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),D,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),D,A),C,A).
% 0.20/0.55 Following clause subsumed by 679 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_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(C,A),D,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)| -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(C,A),c_HOL_Oinverse__class_Odivide(B,D,A),A).
% 0.20/0.55 Following clause subsumed by 680 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,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),D,A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A).
% 0.20/0.55 Following clause subsumed by 707 during input processing: 0 [] {-} A=B|c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat).
% 0.20/0.55 Following clause subsumed by 718 during input processing: 0 [] {-} -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 0.20/0.55 Following clause subsumed by 719 during input processing: 0 [] {-} -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 0.20/0.55 Following clause subsumed by 717 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 0.20/0.55 Following clause subsumed by 723 during input processing: 0 [] {-} -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,E,A),c_HOL_Otimes__class_Otimes(D,C,A),A)|C=E|B=D.
% 0.20/0.55 Following clause subsumed by 734 during input processing: 0 [flip.2] {-} -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Ouminus__class_Ouminus(C,A),A).
% 0.20/0.55 Following clause subsumed by 736 during input processing: 0 [flip.2] {-} -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(B,C,A),A)=c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(B,A),C,A).
% 0.20/0.55 Following clause subsumed by 741 during input processing: 0 [] {-} -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A).
% 0.20/0.55 Following clause subsumed by 742 during input processing: 0 [] {-} -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Oplus__class_Oplus(C,D,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A).
% 0.20/0.55 Following clause subsumed by 738 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A).
% 0.20/0.55 Following clause subsumed by 752 during input processing: 0 [] {-} -class_Ring__and__Field_Ono__zero__divisors(A)|c_HOL_Otimes__class_Otimes(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A).
% 0.20/0.55 Following clause subsumed by 758 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A)=B.
% 0.20/0.55 Following clause subsumed by 763 during input processing: 0 [] {-} -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(B,C,A),A).
% 0.20/0.55 Following clause subsumed by 766 during input processing: 0 [] {-} -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Ominus__class_Ominus(C,D,A),A)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A).
% 0.20/0.55 Following clause subsumed by 767 during input processing: 0 [] {-} -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),D,A)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A).
% 0.20/0.55 Following clause subsumed by 754 during input processing: 0 [flip.2] {-} -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,A),C,A),D,A)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),D,A).
% 0.20/0.55 Following clause subsumed by 694 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(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,A),A),c_Int_Onumber__class_Onumber__of(B,A),A)=c_HOL_Ozero__class_Ozero(A).
% 0.20/0.55 Following clause subsumed by 58 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(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),C,A),C,A)=c_Int_Onumber__class_Onumber__of(B,A)|C=c_HOL_Ozero__class_Ozero(A).
% 0.20/0.55 Following clause subsumed by 772 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_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,c_Int_Onumber__class_Onumber__of(C,A),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).
% 0.20/0.55 Following clause subsumed by 58 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(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),C,A),C,A)=c_Int_Onumber__class_Onumber__of(B,A)|C=c_HOL_Ozero__class_Ozero(A).
% 0.20/0.55 Following clause subsumed by 773 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(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),C,A),C,A)=c_Int_Onumber__class_Onumber__of(B,A).
% 0.20/0.55 Following clause subsumed by 58 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(c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(C,A),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).
% 0.20/0.55 Following clause subsumed by 58 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(c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(C,A),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).
% 0.20/0.55 Following clause subsumed by 694 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(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,A),A),c_Int_Onumber__class_Onumber__of(B,A),A)=c_HOL_Ozero__class_Ozero(A).
% 0.20/0.55 Following clause subsumed by 788 during input processing: 0 [flip.1] {-} c_Int_OPls!=c_Int_OMin.
% 0.20/0.55 Following clause subsumed by 790 during input processing: 0 [] {-} c_Int_OBit0(A)!=c_Int_OMin.
% 0.20/0.55 Following clause subsumed by 347 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,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),D,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),D,A),C,A).
% 0.20/0.55 Following clause subsumed by 298 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),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A).
% 0.20/0.55 Following clause subsumed by 797 during input processing: 0 [] {-} -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),C,A)=B|C=c_HOL_Ozero__class_Ozero(A).
% 0.20/0.55 Following clause subsumed by 816 during input processing: 0 [] {-} -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 0.20/0.55 Following clause subsumed by 252 during input processing: 0 [] {-} c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.20/0.55 Following clause subsumed by 252 during input processing: 0 [] {-} c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.20/0.55 Following clause subsumed by 854 during input processing: 0 [] {-} c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(C,A,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat).
% 0.20/0.55 Following clause subsumed by 269 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),c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),A).
% 0.20/0.55 Following clause subsumed by 403 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).
% 0.20/0.55 Following clause subsumed by 401 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).
% 0.20/0.55 Following clause subsumed by 497 during input processing: 0 [] {-} -class_Int_Onumber(A)| -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A)=c_HOL_Ozero__class_Ozero(A)| -c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A).
% 0.20/0.55 Following clause subsumed by 498 during input processing: 0 [] {-} -class_Int_Onumber(A)| -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(C,A),A)!=c_HOL_Ozero__class_Ozero(A)|c_Ring__and__Field_Odvd__class_Odvd(c_Int_Onumber__class_Onumber__of(C,A),c_Int_Onumber__class_Onumber__of(B,A),A).
% 0.20/0.55 Following clause subsumed by 330 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),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).
% 0.20/0.55 Following clause subsumed by 816 during input processing: 0 [] {-} -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 0.20/0.55 Following clause subsumed by 857 during input processing: 0 [] {-} -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 0.20/0.55 Following clause subsumed by 877 during input processing: 0 [flip.3] {-} -class_Ring__and__Field_Ofield(A)| -class_Int_Onumber__ring(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Oinverse__class_Oinverse(C,A),A)=c_HOL_Oinverse__class_Odivide(B,C,A).
% 0.20/0.56 Following clause subsumed by 460 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(B,A),c_Int_Onumber__class_Onumber__of(C,tc_nat),A)=c_Power_Opower__class_Opower(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).
% 0.20/0.56 Following clause subsumed by 34 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)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A)=c_HOL_Ozero__class_Ozero(A)|c_Int_Onumber__class_Onumber__of(B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.20/0.56 Following clause subsumed by 35 during input processing: 0 [] {-} -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A)=c_HOL_Ozero__class_Ozero(A)|c_Int_Onumber__class_Onumber__of(B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.20/0.56 Following clause subsumed by 419 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(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),c_HOL_Ozero__class_Ozero(A),A).
% 0.20/0.56 Following clause subsumed by 418 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(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),c_HOL_Ozero__class_Ozero(A),A).
% 0.20/0.56 Following clause subsumed by 894 during input processing: 0 [] {-} c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,D,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat)|B=D|A=C.
% 0.20/0.56 Following clause subsumed by 895 during input processing: 0 [] {-} c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Otimes__class_Otimes(A,C,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat)|B=C.
% 0.20/0.56 Following clause subsumed by 83 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(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),c_Power_Opower__class_Opower(C,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),A).
% 0.20/0.56 Following clause subsumed by 924 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).
% 0.20/0.56 Following clause subsumed by 933 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A).
% 0.20/0.56 Following clause subsumed by 933 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A).
% 0.20/0.56 Following clause subsumed by 261 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).
% 0.20/0.56 Following clause subsumed by 950 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(c_Power_Opower__class_Opower(D,B,A),c_Power_Opower__class_Opower(D,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A).
% 0.20/0.56 Following clause subsumed by 951 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A)| -c_HOL_Oord__class_Oless(C,D,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A).
% 0.20/0.56 Following clause subsumed by 599 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,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),D,A),A)| -c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),D,A),C,A).
% 0.20/0.56 Following clause subsumed by 600 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).
% 0.20/0.56 Following clause subsumed by 601 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).
% 0.20/0.56 Following clause subsumed by 503 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(c_HOL_Otimes__class_Otimes(D,c_Int_Onumber__class_Onumber__of(C,A),A),B,A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(C,A),A).
% 0.20/0.56 Following clause subsumed by 505 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,c_HOL_Otimes__class_Otimes(B,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).
% 0.20/0.56 Following clause subsumed by 965 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).
% 0.20/0.56 Following clause subsumed by 964 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).
% 0.20/0.56 Following clause subsumed by 504 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,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(D,A),C,A),A).
% 0.20/0.56 Following clause subsumed by 503 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(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(D,A),C,A),B,A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A).
% 0.20/0.56 Following clause subsumed by 602 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(c_HOL_Otimes__class_Otimes(D,c_Int_Onumber__class_Onumber__of(C,A),A),B,A)| -c_lessequals(B,c_HOL_Otimes__class_Otimes(D,c_Int_Onumber__class_Onumber__of(C,A),A),A).
% 0.20/0.56 Following clause subsumed by 599 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,c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(D,A),A),A)| -c_lessequals(c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(D,A),A),C,A).
% 0.20/0.56 Following clause subsumed by 502 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),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).
% 0.20/0.56 Following clause subsumed by 221 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),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A),A)| -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat).
% 0.20/0.56 Following clause subsumed by 452 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(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 0.20/0.56 Following clause subsumed by 551 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A)| -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A)|c_Parity_Oeven__odd__class_Oeven(C,tc_nat).
% 0.20/0.56 Following clause subsumed by 1001 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),c_Power_Opower__class_Opower(B,C,A),A)|c_Parity_Oeven__odd__class_Oeven(C,tc_nat).
% 0.20/0.56 Following clause subsumed by 551 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__idom(A)|c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A)| -c_lessequals(c_HOL_Ozero__class_Ozero(A),B,A)|c_Parity_Oeven__odd__class_Oeven(C,tc_nat).
% 0.20/0.56 Following clause subsumed by 1001 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),c_Power_Opower__class_Opower(B,C,A),A).
% 0.20/0.56 Following clause subsumed by 694 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_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 0.20/0.56 Following clause subsumed by 49 during input processing: 0 [] {-} c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).
% 0.20/0.56 Following clause subsumed by 49 during input processing: 0 [] {-} c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).
% 0.20/0.59 Following clause subsumed by 1012 during input processing: 0 [] {-} -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 0.20/0.59 Following clause subsumed by 886 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)|c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 0.20/0.59 Following clause subsumed by 1036 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.
% 0.20/0.59 Following clause subsumed by 1065 during input processing: 0 [] {-} c_Int_OBit1(A)!=c_Int_OPls.
% 0.20/0.59 Following clause subsumed by 1073 during input processing: 0 [flip.2] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A).
% 0.20/0.59 Following clause subsumed by 1073 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A).
% 0.20/0.59 Following clause subsumed by 1074 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)=c_HOL_Otimes__class_Otimes(D,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),E,A),A).
% 0.20/0.59 Following clause subsumed by 1073 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,c_HOL_Otimes__class_Otimes(D,E,A),A),A).
% 0.20/0.59 Following clause subsumed by 1089 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,C,A)=c_HOL_Otimes__class_Otimes(C,B,A).
% 0.20/0.59 49 back subsumes 48.
% 0.20/0.59 160 back subsumes 157.
% 0.20/0.59 161 back subsumes 159.
% 0.20/0.59 182 back subsumes 181.
% 0.20/0.59 249 back subsumes 215.
% 0.20/0.59 343 back subsumes 290.
% 0.20/0.59 343 back subsumes 266.
% 0.20/0.59 344 back subsumes 265.
% 0.20/0.59 347 back subsumes 289.
% 0.20/0.59 348 back subsumes 264.
% 0.20/0.59 403 back subsumes 402.
% 0.20/0.59 504 back subsumes 222.
% 0.20/0.59 505 back subsumes 184.
% 0.20/0.59 506 back subsumes 223.
% 0.20/0.59 506 back subsumes 183.
% 0.20/0.59 551 back subsumes 226.
% 0.20/0.59 553 back subsumes 122.
% 0.20/0.59 600 back subsumes 33.
% 0.20/0.59 601 back subsumes 32.
% 0.20/0.59 602 back subsumes 19.
% 0.20/0.59 603 back subsumes 31.
% 0.20/0.59 603 back subsumes 20.
% 0.20/0.59 604 back subsumes 30.
% 0.20/0.59 604 back subsumes 21.
% 0.20/0.59 675 back subsumes 515.
% 0.20/0.59 675 back subsumes 263.
% 0.20/0.59 676 back subsumes 516.
% 0.20/0.59 676 back subsumes 262.
% 0.20/0.59 677 back subsumes 652.
% 0.20/0.59 677 back subsumes 650.
% 0.20/0.59 678 back subsumes 651.
% 0.20/0.59 678 back subsumes 286.
% 0.20/0.59 679 back subsumes 517.
% 0.20/0.59 680 back subsumes 518.
% 0.20/0.59 681 back subsumes 653.
% 0.20/0.59 682 back subsumes 285.
% 0.20/0.59 797 back subsumes 772.
% 0.20/0.59 825 back subsumes 824.
% 0.20/0.59 850 back subsumes 461.
% 0.20/0.59 864 back subsumes 863.
% 0.20/0.59 899 back subsumes 855.
% 0.20/0.59 901 back subsumes 582.
% 0.20/0.59 901 back subsumes 457.
% 0.20/0.59 958 back subsumes 645.
% 0.20/0.59 958 back subsumes 296.
% 0.20/0.59 959 back subsumes 646.
% 0.20/0.59 959 back subsumes 297.
% 0.20/0.59 960 back subsumes 794.
% 0.20/0.59 960 back subsumes 647.
% 0.20/0.59 961 back subsumes 793.
% 0.20/0.59 961 back subsumes 648.
% 0.20/0.59 1001 back subsumes 227.
% 0.20/0.59 Following clause subsumed by 1093 during input processing: 0 [copy,1071,flip.1] {-} c_Int_OBit0(A)!=c_Int_OBit1(B).
% 0.20/0.59 1077 back subsumes 1066.
% 0.20/0.59 Following clause subsumed by 1071 during input processing: 0 [copy,1093,flip.1] {-} c_Int_OBit1(A)!=c_Int_OBit0(B).
% 0.20/0.59 1163 back subsumes 1162.
% 0.20/0.59
% 0.20/0.59 ------------> process sos:
% 0.20/0.59 Following clause subsumed by 1288 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(A,c_Suc(A),tc_nat).
% 0.20/0.59 Following clause subsumed by 1296 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 0.20/0.59 Following clause subsumed by 1295 during input processing: 0 [] {-} c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 0.20/0.59 Following clause subsumed by 1308 during input processing: 0 [] {-} c_HOL_Oord__class_Oless(A,c_Suc(c_HOL_Oplus__class_Oplus(A,B,tc_nat)),tc_nat).
% 0.20/0.59 Following clause subsumed by 1332 during input processing: 0 [] {-} c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)|c_Parity_Oeven__odd__class_Oeven(B,tc_nat)|c_Parity_Oeven__odd__class_Oeven(A,tc_nat).
% 0.20/0.59 Following clause subsumed by 1332 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(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat).
% 0.20/0.59 Following clause subsumed by 1344 during input processing: 0 [demod,1313] {-} c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat),tc_nat).
% 0.20/0.59 Following clause subsumed by 1295 during input processing: 0 [] {-} c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 0.20/0.59 Following clause subsumed by 1322 during input processing: 0 [demod,1313,1321,1313] {-} c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),B,tc_nat),tc_nat).
% 0.20/0.59 Following clause subsumed by 1366 during input processing: 0 [demod,1313,1321,1313] {-} c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat).
% 0.20/0.59 Following clause subsumed by 1322 during input processing: 0 [demod,1313,1313] {-} c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),B,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat).
% 0.20/0.59 Following clause subsumed by 1366 during input processing: 0 [demod,1355,1313,1364] {-} c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 0.20/0.59 Following clause subsumed by 1366 during input processing: 0 [demod,1381] {-} c_Int_OMin=c_Int_OMin.
% 0.20/0.59 Following clause subsumed by 1366 during input processing: 0 [demod,1355,1313,1364,1355,1313,1364,1355,1364] {-} c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 0.20/0.59 Following clause subsumed by 1366 during input processing: 0 [demod,1355,1413,1355,1413] {-} c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat).
% 0.20/0.59 Following clause subsumed by 1366 during input processing: 0 [demod,1355,1416,1355,1416] {-} c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat).
% 0.20/0.59 Following clause subsumed by 1366 during input processing: 0 [demod,1386] {-} c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 0.20/0.59 Following clause subsumed by 1372 during input processing: 0 [] {-} c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat).
% 0.20/0.59 Following clause subsumed by 1372 during input processing: 0 [] {-} c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat).
% 0.20/0.59 Following clause subsumed by 1366 during input processing: 0 [demod,1418,1321] {-} c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,B,tc_nat),D,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,B,tc_nat),D,tc_nat),tc_nat).
% 0.20/0.59 Following clause subsumed by 1366 during input processing: 0 [demod,1424] {-} c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 0.43/0.61 Following clause subsumed by 1366 during input processing: 0 [demod,1313,1313,1313,1436,1321,1321] {-} c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat),tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat),tc_nat),tc_nat).
% 0.43/0.61 Following clause subsumed by 1366 during input processing: 0 [demod,1355,1355,1313,1364,1369,1355,1313,1364] {-} c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 0.43/0.61 Following clause subsumed by 1366 during input processing: 0 [demod,1442] {-} c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 0.43/0.61 Following clause subsumed by 1366 during input processing: 0 [demod,1442,1321,1313,1313] {-} c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat),tc_nat).
% 0.43/0.61 Following clause subsumed by 1366 during input processing: 0 [demod,1468,1355] {-} c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat).
% 0.43/0.61 Following clause subsumed by 1366 during input processing: 0 [demod,1433] {-} c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 0.43/0.61 Following clause subsumed by 1366 during input processing: 0 [demod,1433] {-} c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 0.43/0.61 Following clause subsumed by 1366 during input processing: 0 [demod,1457,1465,1420,1424,1424] {-} c_HOL_Oplus__class_Oplus(A,A,tc_nat)=c_HOL_Oplus__class_Oplus(A,A,tc_nat).
% 0.43/0.61 Following clause subsumed by 1366 during input processing: 0 [demod,1457,1465,1418,1422,1422] {-} c_HOL_Oplus__class_Oplus(A,A,tc_nat)=c_HOL_Oplus__class_Oplus(A,A,tc_nat).
% 0.43/0.61 Following clause subsumed by 1366 during input processing: 0 [demod,1476] {-} c_Int_OPls=c_Int_OPls.
% 0.43/0.61 Following clause subsumed by 1366 during input processing: 0 [] {-} A=A.
% 0.43/0.61 Following clause subsumed by 1372 during input processing: 0 [copy,1315,flip.1] {-} c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat).
% 0.43/0.61 Following clause subsumed by 1322 during input processing: 0 [copy,1322,flip.1] {-} c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat).
% 0.43/0.61 Following clause subsumed by 1366 during input processing: 0 [copy,1366,flip.1] {-} A=A.
% 0.43/0.61 1366 back subsumes 1281.
% 0.43/0.61 1366 back subsumes 1139.
% 0.43/0.61 1366 back subsumes 1130.
% 0.43/0.61 1366 back subsumes 1129.
% 0.43/0.61 1366 back subsumes 1128.
% 0.43/0.61 1366 back subsumes 1105.
% 0.43/0.61 1366 back subsumes 1104.
% 0.43/0.61 1366 back subsumes 1103.
% 0.43/0.61 1366 back subsumes 1102.
% 0.43/0.61 Following clause subsumed by 1372 during input processing: 0 [copy,1372,flip.1] {-} c_HOL_Oplus__class_Oplus(A,B,tc_nat)=c_HOL_Oplus__class_Oplus(B,A,tc_nat).
% 0.43/0.61 1372 back subsumes 1315.
% 0.43/0.61 1471 back subsumes 1179.
% 0.43/0.61 Following clause subsumed by 1479 during input processing: 0 [copy,1479,flip.1] {-} c_HOL_Otimes__class_Otimes(A,B,tc_nat)=c_HOL_Otimes__class_Otimes(B,A,tc_nat).
% 0.43/0.61 Following clause subsumed by 1749 during input processing: 0 [copy,1748,flip.1] {-} c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat),B,tc_nat)=c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat),B,tc_nat).
% 0.43/0.61 Following clause subsumed by 1748 during input processing: 0 [copy,1749,flip.1] {-} c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat),B,tc_nat)=c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat),B,tc_nat).
% 0.43/0.61 Following clause subsumed by 1410 during input processing: 0 [copy,1754,flip.1] {-} c_Divides_Odiv__class_Odiv(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(A,B,tc_nat),C,tc_nat).
% 0.43/0.61 Following clause subsumed by 1444 during input processing: 0 [copy,1806,flip.1] {-} c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_Divides_Odiv__class_Odiv(A,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat).
% 0.43/0.61 Following clause subsumed by 1449 during input processing: 0 [copy,1807,flip.1] {-} c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),A,tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat).
% 0.43/0.61 Following clause subsumed by 1454 during input processing: 0 [copy,1808,flip.1] {-} c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat),tc_nat).
% 0.43/0.61 Following clause subsumed by 1820 during input processing: 0 [copy,1819,flip.1] {-} c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(A),A,tc_Complex_Ocomplex)=c_FFT__Mirabelle_Oroot(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)).
% 0.43/0.61 Following clause subsumed by 1819 during input processing: 0 [copy,1820,flip.1] {-} c_FFT__Mirabelle_Oroot(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat))=c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(A),A,tc_Complex_Ocomplex).
% 0.43/0.61
% 0.43/0.61 ======= end of input processing =======
% 0.60/0.85
% 0.60/0.85
% 0.60/0.85
% 0.60/0.85 Aborting on detection of an error:
% 0.60/0.85
% 0.60/0.85 Too many clauses (whew!).
% 0.60/0.85
%------------------------------------------------------------------------------