TSTP Solution File: SWW196+1 by SOS---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SOS---2.0
% Problem : SWW196+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : sos-script %s
% Computer : n029.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 : Thu Jul 21 01:26:20 EDT 2022
% Result : Theorem 0.37s 0.57s
% Output : Refutation 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW196+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : sos-script %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 6 02:00:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.17/0.49 ----- Otter 3.2, August 2001 -----
% 0.17/0.49 The process was started by sandbox2 on n029.cluster.edu,
% 0.17/0.49 Mon Jun 6 02:00:19 2022
% 0.17/0.49 The command was "./sos". The process ID is 8808.
% 0.17/0.49
% 0.17/0.49 set(prolog_style_variables).
% 0.17/0.49 set(auto).
% 0.17/0.49 dependent: set(auto1).
% 0.17/0.49 dependent: set(process_input).
% 0.17/0.49 dependent: clear(print_kept).
% 0.17/0.49 dependent: clear(print_new_demod).
% 0.17/0.49 dependent: clear(print_back_demod).
% 0.17/0.49 dependent: clear(print_back_sub).
% 0.17/0.49 dependent: set(control_memory).
% 0.17/0.49 dependent: assign(max_mem, 12000).
% 0.17/0.49 dependent: assign(pick_given_ratio, 4).
% 0.17/0.49 dependent: assign(stats_level, 1).
% 0.17/0.49 dependent: assign(pick_semantic_ratio, 3).
% 0.17/0.49 dependent: assign(sos_limit, 5000).
% 0.17/0.49 dependent: assign(max_weight, 60).
% 0.17/0.49 clear(print_given).
% 0.17/0.49
% 0.17/0.49 formula_list(usable).
% 0.17/0.49
% 0.17/0.49 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 0.17/0.49
% 0.17/0.49 This ia a non-Horn set with equality. The strategy will be
% 0.17/0.49 Knuth-Bendix, ordered hyper_res, ur_res, factoring, and
% 0.17/0.49 unit deletion, with positive clauses in sos and nonpositive
% 0.17/0.49 clauses in usable.
% 0.17/0.49
% 0.17/0.49 dependent: set(knuth_bendix).
% 0.17/0.49 dependent: set(para_from).
% 0.17/0.49 dependent: set(para_into).
% 0.17/0.49 dependent: clear(para_from_right).
% 0.17/0.49 dependent: clear(para_into_right).
% 0.17/0.49 dependent: set(para_from_vars).
% 0.17/0.49 dependent: set(eq_units_both_ways).
% 0.17/0.49 dependent: set(dynamic_demod_all).
% 0.17/0.49 dependent: set(dynamic_demod).
% 0.17/0.49 dependent: set(order_eq).
% 0.17/0.49 dependent: set(back_demod).
% 0.17/0.49 dependent: set(lrpo).
% 0.17/0.49 dependent: set(hyper_res).
% 0.17/0.49 dependent: set(unit_deletion).
% 0.17/0.49 dependent: set(factor).
% 0.17/0.49
% 0.17/0.49 ------------> process usable:
% 0.17/0.49 Following clause subsumed by 16 during input processing: 0 [] {-} c_Int_OBit1(A)!=c_Int_OPls.
% 0.17/0.49 Following clause subsumed by 17 during input processing: 0 [flip.2] {-} -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(A,c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,C))=c_Groups_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)).
% 0.17/0.49 Following clause subsumed by 19 during input processing: 0 [] {-} -class_Int_Onumber__ring(A)|c_Groups_Ozero__class_Ozero(A)=c_Int_Onumber__class_Onumber__of(A,c_Int_OPls).
% 0.17/0.49 Following clause subsumed by 39 during input processing: 0 [] {-} c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)!=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=C.
% 0.17/0.49 Following clause subsumed by 41 during input processing: 0 [] {-} c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 0.17/0.49 Following clause subsumed by 40 during input processing: 0 [] {-} c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C)|B!=C.
% 0.17/0.49 Following clause subsumed by 47 during input processing: 0 [] {-} -class_RealVector_Oreal__normed__algebra(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A),B)=c_Groups_Ozero__class_Ozero(A).
% 0.17/0.49 Following clause subsumed by 50 during input processing: 0 [] {-} -class_RealVector_Oreal__normed__algebra(A)|c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 0.17/0.49 Following clause subsumed by 54 during input processing: 0 [] {-} -class_Rings_Ono__zero__divisors(A)|c_Groups_Otimes__class_Otimes(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 0.17/0.49 Following clause subsumed by 59 during input processing: 0 [flip.2] {-} -class_Rings_Ocomm__semiring__1(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,B,C),D)=c_Groups_Otimes__class_Otimes(A,B,c_Groups_Otimes__class_Otimes(A,C,D)).
% 0.17/0.49 Following clause subsumed by 79 during input processing: 0 [] {-} -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D)).
% 0.17/0.49 Following clause subsumed by 88 during input processing: 0 [] {-} -class_Rings_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(A,B,c_Nat_OSuc(C))=c_Groups_Otimes__class_Otimes(A,B,c_Power_Opower__class_Opower(A,B,C)).
% 0.17/0.49 Following clause subsumed by 92 during input processing: 0 [] {-} c_Nat_OSuc(A)!=A.
% 0.17/0.49 Following clause subsumed by 95 during input processing: 0 [] {-} -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|A=B.
% 0.17/0.49 Following clause subsumed by 93 during input processing: 0 [] {-} c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|A!=B.
% 0.17/0.49 Following clause subsumed by 94 during input processing: 0 [] {-} -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|A!=B.
% 0.17/0.49 Following clause subsumed by 95 during input processing: 0 [] {-} -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|B=A.
% 0.17/0.49 Following clause subsumed by 95 during input processing: 0 [] {-} A=B| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A).
% 0.17/0.49 Following clause subsumed by 93 during input processing: 0 [] {-} A!=B|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B).
% 0.17/0.49 Following clause subsumed by 95 during input processing: 0 [] {-} -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|B=A.
% 0.17/0.49 Following clause subsumed by 93 during input processing: 0 [] {-} -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|B!=A.
% 0.17/0.49 Following clause subsumed by 95 during input processing: 0 [] {-} -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|A=B.
% 0.17/0.49 Following clause subsumed by 95 during input processing: 0 [] {-} -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|A=B| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A).
% 0.17/0.49 Following clause subsumed by 95 during input processing: 0 [] {-} -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|A=B.
% 0.17/0.49 Following clause subsumed by 95 during input processing: 0 [] {-} -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|A=B.
% 0.17/0.49 Following clause subsumed by 104 during input processing: 0 [] {-} A!=B| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,C,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,C).
% 0.17/0.49 Following clause subsumed by 105 during input processing: 0 [] {-} A!=B| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,C,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,C,A).
% 0.17/0.49 Following clause subsumed by 106 during input processing: 0 [] {-} -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,C,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,C).
% 0.17/0.49 Following clause subsumed by 106 during input processing: 0 [] {-} -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,C,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,C,A).
% 0.17/0.49 Following clause subsumed by 98 during input processing: 0 [] {-} c_Nat_OSuc(A)!=c_Nat_OSuc(B)|A=B.
% 0.17/0.49 Following clause subsumed by 94 during input processing: 0 [] {-} -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|A!=B.
% 0.17/0.49 Following clause subsumed by 94 during input processing: 0 [] {-} -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|A!=B.
% 0.17/0.49 Following clause subsumed by 93 during input processing: 0 [] {-} -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|B!=A.
% 0.17/0.49 Following clause subsumed by 105 during input processing: 0 [] {-} -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|B!=C|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,C).
% 0.17/0.49 Following clause subsumed by 104 during input processing: 0 [] {-} -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)|B!=C| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,C,A).
% 0.17/0.49 Following clause subsumed by 106 during input processing: 0 [] {-} -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,C).
% 0.17/0.49 Following clause subsumed by 106 during input processing: 0 [] {-} -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,C,A).
% 0.17/0.49 Following clause subsumed by 106 during input processing: 0 [] {-} -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,C,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,C).
% 0.17/0.49 Following clause subsumed by 106 during input processing: 0 [] {-} -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,B)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,A)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,C,B)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,C,A).
% 0.17/0.49 Following clause subsumed by 113 during input processing: 0 [] {-} -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C))=c_Groups_Oplus__class_Oplus(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C)).
% 0.17/0.49 Following clause subsumed by 93 during input processing: 0 [] {-} c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|A!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 0.17/0.49 Following clause subsumed by 107 during input processing: 0 [] {-} -c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,B))|c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,A).
% 0.17/0.49 Following clause subsumed by 156 during input processing: 0 [] {-} -class_RealVector_Oreal__normed__algebra(A)|c_Groups_Otimes__class_Otimes(A,B,c_Groups_Oplus__class_Oplus(A,C,D))=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)).
% 0.17/0.49 Following clause subsumed by 163 during input processing: 0 [] {-} -class_RealVector_Oreal__normed__algebra(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,D)).
% 0.17/0.49 Following clause subsumed by 162 during input processing: 0 [flip.2] {-} -class_Rings_Ocomm__semiring__1(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,D),C)=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C)).
% 0.17/0.49 Following clause subsumed by 158 during input processing: 0 [] {-} -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,E))!=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,E),c_Groups_Otimes__class_Otimes(A,D,C))|B=D|C=E.
% 0.17/0.49 Following clause subsumed by 159 during input processing: 0 [] {-} -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,E))=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,E),c_Groups_Otimes__class_Otimes(A,D,C))|B!=D.
% 0.17/0.49 Following clause subsumed by 160 during input processing: 0 [] {-} -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,E))=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,E),c_Groups_Otimes__class_Otimes(A,D,C))|C!=E.
% 0.17/0.49 Following clause subsumed by 166 during input processing: 0 [flip.1] {-} c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 0.17/0.49 Following clause subsumed by 166 during input processing: 0 [] {-} c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 0.17/0.49 Following clause subsumed by 166 during input processing: 0 [] {-} c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 0.17/0.49 Following clause subsumed by 166 during input processing: 0 [flip.1] {-} c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 0.17/0.49 Following clause subsumed by 166 during input processing: 0 [flip.1] {-} c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 0.17/0.49 Following clause subsumed by 172 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit1(B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B).
% 0.17/0.49 Following clause subsumed by 173 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit1(B))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B).
% 0.17/0.49 Following clause subsumed by 175 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit0(B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B).
% 0.17/0.49 Following clause subsumed by 176 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit0(B))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B).
% 0.17/0.49 Following clause subsumed by 40 during input processing: 0 [] {-} c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(A),B)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(A),C)|B!=C.
% 0.17/0.49 Following clause subsumed by 182 during input processing: 0 [] {-} -c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))| -c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,A)|c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,B).
% 0.17/0.49 Following clause subsumed by 181 during input processing: 0 [] {-} -c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))|c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,A)| -c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,B).
% 0.17/0.49 Following clause subsumed by 183 during input processing: 0 [] {-} c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))| -c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,A)| -c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,B).
% 0.17/0.49 Following clause subsumed by 183 during input processing: 0 [] {-} c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))| -c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,A)| -c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,B).
% 0.17/0.49 Following clause subsumed by 181 during input processing: 0 [] {-} -c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))|c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,A)| -c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,B).
% 0.17/0.49 Following clause subsumed by 182 during input processing: 0 [] {-} -c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))| -c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,A)|c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,B).
% 0.17/0.49 Following clause subsumed by 184 during input processing: 0 [] {-} -c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B))|c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,A)|c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,B).
% 0.17/0.49 Following clause subsumed by 186 during input processing: 0 [] {-} c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B))| -c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,A).
% 0.17/0.49 Following clause subsumed by 185 during input processing: 0 [] {-} c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B))| -c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,B).
% 0.17/0.49 Following clause subsumed by 135 during input processing: 0 [] {-} -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)),c_Groups_Ozero__class_Ozero(A))| -c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)).
% 0.17/0.49 Following clause subsumed by 136 during input processing: 0 [] {-} -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 0.17/0.49 Following clause subsumed by 137 during input processing: 0 [] {-} -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)),c_Groups_Ozero__class_Ozero(A))|c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 0.17/0.49 Following clause subsumed by 191 during input processing: 0 [] {-} -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)))|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 0.17/0.49 Following clause subsumed by 192 during input processing: 0 [] {-} -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)))|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Groups_Ozero__class_Ozero(A)| -c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)).
% 0.17/0.49 Following clause subsumed by 193 during input processing: 0 [] {-} -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)))|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Groups_Ozero__class_Ozero(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 0.17/0.49 Following clause subsumed by 194 during input processing: 0 [] {-} -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)))|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 0.17/0.49 Following clause subsumed by 195 during input processing: 0 [] {-} -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)))| -c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))|B=c_Groups_Ozero__class_Ozero(A).
% 0.17/0.49 Following clause subsumed by 196 during input processing: 0 [] {-} -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)))|c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 0.17/0.49 Following clause subsumed by 217 during input processing: 0 [] {-} -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D))| -c_Orderings_Oord__class_Oless(A,D,C).
% 0.17/0.49 Following clause subsumed by 223 during input processing: 0 [] {-} -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,C,B),c_Groups_Ozero__class_Ozero(A)).
% 0.17/0.49 Following clause subsumed by 230 during input processing: 0 [] {-} -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,D).
% 0.17/0.49 Following clause subsumed by 217 during input processing: 0 [] {-} -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,D,C).
% 0.17/0.50 Following clause subsumed by 218 during input processing: 0 [] {-} -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,D,B).
% 0.17/0.50 Following clause subsumed by 254 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit0(B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B).
% 0.17/0.50 Following clause subsumed by 255 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit0(B))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B).
% 0.17/0.50 Following clause subsumed by 308 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 0.17/0.50 Following clause subsumed by 308 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 0.17/0.50 Following clause subsumed by 316 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,A,B))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 0.17/0.50 Following clause subsumed by 318 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,A,B))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 0.17/0.50 Following clause subsumed by 317 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,A,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 0.17/0.50 Following clause subsumed by 324 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|A=B.
% 0.17/0.50 Following clause subsumed by 322 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),c_Nat_OSuc(B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 0.17/0.50 Following clause subsumed by 309 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),c_Nat_OSuc(B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 0.17/0.50 Following clause subsumed by 324 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A=B.
% 0.17/0.50 Following clause subsumed by 327 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 0.17/0.50 Following clause subsumed by 346 during input processing: 0 [] {-} -c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,A)| -c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,B)|c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)).
% 0.17/0.50 Following clause subsumed by 345 during input processing: 0 [] {-} -c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,A)|c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,B)| -c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)).
% 0.17/0.50 Following clause subsumed by 344 during input processing: 0 [] {-} c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,A)| -c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,B)| -c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)).
% 0.17/0.50 Following clause subsumed by 343 during input processing: 0 [] {-} -c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,C))|A=c_Groups_Ozero__class_Ozero(tc_Int_Oint)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,B,C).
% 0.17/0.50 Following clause subsumed by 352 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 0.17/0.50 Following clause subsumed by 316 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)))|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 0.17/0.50 Following clause subsumed by 318 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)))|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 0.17/0.50 Following clause subsumed by 317 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 0.17/0.50 Following clause subsumed by 337 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 0.17/0.50 Following clause subsumed by 336 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B).
% 0.17/0.50 Following clause subsumed by 40 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C)|B!=C.
% 0.17/0.50 Following clause subsumed by 367 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 0.17/0.50 Following clause subsumed by 368 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 0.17/0.50 Following clause subsumed by 371 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C)).
% 0.17/0.50 Following clause subsumed by 368 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,A),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)).
% 0.17/0.50 Following clause subsumed by 367 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(A),B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(A),C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 0.17/0.50 Following clause subsumed by 245 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C))| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C).
% 0.17/0.50 Following clause subsumed by 382 during input processing: 0 [] {-} -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C).
% 0.17/0.50 Following clause subsumed by 388 during input processing: 0 [] {-} -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,B,D)|C=D.
% 0.17/0.50 Following clause subsumed by 390 during input processing: 0 [] {-} -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,D,C)|B=D.
% 0.17/0.50 Following clause subsumed by 406 during input processing: 0 [] {-} -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless(A,B,D).
% 0.17/0.50 Following clause subsumed by 408 during input processing: 0 [] {-} -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless(A,C,D).
% 0.17/0.50 Following clause subsumed by 443 during input processing: 0 [] {-} -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -c_Orderings_Oord__class_Oless__eq(A,c_Power_Opower__class_Opower(A,B,C),c_Power_Opower__class_Opower(A,B,D))|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,C,D).
% 0.17/0.50 Following clause subsumed by 447 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)|c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B).
% 0.17/0.50 Following clause subsumed by 446 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,A,B)| -c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,A,B)|A=B.
% 0.17/0.50 Following clause subsumed by 451 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B.
% 0.17/0.50 Following clause subsumed by 454 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A=B.
% 0.17/0.50 Following clause subsumed by 453 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 0.17/0.50 Following clause subsumed by 450 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,A).
% 0.17/0.50 Following clause subsumed by 452 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=A.
% 0.17/0.50 Following clause subsumed by 451 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B.
% 0.17/0.50 Following clause subsumed by 453 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B).
% 0.17/0.50 Following clause subsumed by 454 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B)|A=B|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 0.17/0.50 Following clause subsumed by 457 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 0.17/0.50 Following clause subsumed by 453 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B).
% 0.17/0.50 Following clause subsumed by 455 during input processing: 0 [] {-} A!=B|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B).
% 0.17/0.50 Following clause subsumed by 474 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),C)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C),A).
% 0.17/0.50 Following clause subsumed by 476 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B),A).
% 0.17/0.50 Following clause subsumed by 506 during input processing: 0 [] {-} c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B).
% 0.17/0.50 Following clause subsumed by 539 during input processing: 0 [] {-} c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)!=c_Groups_Oone__class_Oone(tc_Int_Oint)|A=c_Groups_Oone__class_Oone(tc_Int_Oint)|A=c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin).
% 0.17/0.50 Following clause subsumed by 545 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Oone__class_Oone(tc_Int_Oint)),B)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B).
% 0.17/0.50 Following clause subsumed by 557 during input processing: 0 [] {-} -class_RealVector_Oreal__normed__algebra(A)|c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ominus__class_Ominus(A,C,D))=c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)).
% 0.17/0.50 Following clause subsumed by 558 during input processing: 0 [] {-} -class_RealVector_Oreal__normed__algebra(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,C),D)=c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,D)).
% 0.17/0.50 Following clause subsumed by 563 during input processing: 0 [flip.2] {-} -class_Rings_Ozero__neq__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A).
% 0.17/0.50 Following clause subsumed by 575 during input processing: 0 [] {-} c_Int_OPls!=c_Int_OMin.
% 0.17/0.50 Following clause subsumed by 583 during input processing: 0 [] {-} c_Int_OBit0(A)!=c_Int_OMin.
% 0.17/0.50 Following clause subsumed by 584 during input processing: 0 [] {-} -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless__eq(A,C,D).
% 0.17/0.50 Following clause subsumed by 585 during input processing: 0 [] {-} -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless__eq(A,B,D).
% 0.17/0.50 Following clause subsumed by 455 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 0.17/0.50 Following clause subsumed by 598 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit1(B))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B).
% 0.17/0.50 Following clause subsumed by 599 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit1(B))| -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B).
% 0.17/0.50 Following clause subsumed by 455 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Nat_OSuc(B))|A!=c_Nat_OSuc(B).
% 0.17/0.50 Following clause subsumed by 604 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Nat_OSuc(B)).
% 0.17/0.50 Following clause subsumed by 603 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,c_Nat_OSuc(B))|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B)|A=c_Nat_OSuc(B).
% 0.17/0.50 Following clause subsumed by 609 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(A),B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 0.17/0.50 Following clause subsumed by 608 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(A),B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 0.17/0.50 Following clause subsumed by 611 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B)).
% 0.17/0.50 Following clause subsumed by 608 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(A),B).
% 0.17/0.50 Following clause subsumed by 330 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Nat_OSuc(A))|B!=A.
% 0.17/0.50 Following clause subsumed by 609 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(A),B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 0.17/0.50 Following clause subsumed by 613 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit0(B))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B).
% 0.17/0.50 Following clause subsumed by 614 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit0(B))| -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B).
% 0.17/0.50 Following clause subsumed by 625 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C).
% 0.17/0.50 Following clause subsumed by 624 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C).
% 0.17/0.50 Following clause subsumed by 652 during input processing: 0 [] {-} -class_Int_Onumber__ring(A)| -c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,B)|c_Power_Opower__class_Opower(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OMin),B)=c_Groups_Oone__class_Oone(A).
% 0.17/0.50 Following clause subsumed by 671 during input processing: 0 [] {-} -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)).
% 0.17/0.50 Following clause subsumed by 669 during input processing: 0 [] {-} -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 0.17/0.50 Following clause subsumed by 669 during input processing: 0 [] {-} -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,C,B),c_Groups_Ozero__class_Ozero(A)).
% 0.17/0.50 Following clause subsumed by 668 during input processing: 0 [] {-} -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__eq(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__eq(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 0.17/0.50 Following clause subsumed by 722 during input processing: 0 [] {-} -hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)|hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 0.17/0.50 Following clause subsumed by 723 during input processing: 0 [] {-} -hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))|B!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,D)|hBOOL(hAPP(A,D)).
% 0.17/0.50 Following clause subsumed by 733 during input processing: 0 [] {-} -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -c_Orderings_Oord__class_Oless(A,c_Power_Opower__class_Opower(A,B,C),c_Power_Opower__class_Opower(A,B,D))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D).
% 0.17/0.50 Following clause subsumed by 732 during input processing: 0 [] {-} -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)|c_Orderings_Oord__class_Oless(A,c_Power_Opower__class_Opower(A,B,C),c_Power_Opower__class_Opower(A,B,D))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D).
% 0.17/0.51 Following clause subsumed by 752 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit1(B))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B).
% 0.17/0.51 Following clause subsumed by 753 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit1(B))| -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B).
% 0.17/0.51 Following clause subsumed by 631 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C))| -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C).
% 0.17/0.51 Following clause subsumed by 630 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B))| -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C).
% 0.17/0.51 Following clause subsumed by 759 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C).
% 0.17/0.51 Following clause subsumed by 631 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C))| -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C).
% 0.17/0.51 Following clause subsumed by 631 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(A),B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(A),C))| -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C).
% 0.17/0.51 Following clause subsumed by 774 during input processing: 0 [] {-} -class_Rings_Ocomm__ring(A)| -class_Rings_Odvd(A)| -c_Rings_Odvd__class_Odvd(A,B,C)| -c_Rings_Odvd__class_Odvd(A,B,c_Groups_Oplus__class_Oplus(A,D,E))|c_Rings_Odvd__class_Odvd(A,B,c_Groups_Oplus__class_Oplus(A,c_Groups_Ominus__class_Ominus(A,D,c_Groups_Otimes__class_Otimes(A,F,C)),E)).
% 0.17/0.51 Following clause subsumed by 775 during input processing: 0 [] {-} -class_Rings_Ocomm__ring(A)| -class_Rings_Odvd(A)| -c_Rings_Odvd__class_Odvd(A,B,C)|c_Rings_Odvd__class_Odvd(A,B,c_Groups_Oplus__class_Oplus(A,D,E))| -c_Rings_Odvd__class_Odvd(A,B,c_Groups_Oplus__class_Oplus(A,c_Groups_Ominus__class_Ominus(A,D,c_Groups_Otimes__class_Otimes(A,F,C)),E)).
% 0.17/0.51 Following clause subsumed by 653 during input processing: 0 [] {-} -class_Int_Onumber__ring(A)|c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,B)|c_Power_Opower__class_Opower(A,c_Int_Onumber__class_Onumber__of(A,c_Int_OMin),B)=c_Int_Onumber__class_Onumber__of(A,c_Int_OMin).
% 0.17/0.51 Following clause subsumed by 819 during input processing: 0 [] {-} -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,B,C))|c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B)|c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,C).
% 0.17/0.51 Following clause subsumed by 819 during input processing: 0 [] {-} -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,B,C))|c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,C)|c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B).
% 0.17/0.51 Following clause subsumed by 823 during input processing: 0 [] {-} -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,B,C))| -c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,C).
% 0.17/0.51 Following clause subsumed by 822 during input processing: 0 [] {-} -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,B,C))|c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,C)| -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B).
% 0.17/0.51 Following clause subsumed by 835 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit1(B))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B).
% 0.17/0.51 Following clause subsumed by 836 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(A),c_Int_OBit1(B))| -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,B).
% 0.17/0.51 Following clause subsumed by 837 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit0(B))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B).
% 0.17/0.51 Following clause subsumed by 838 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(A),c_Int_OBit0(B))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B).
% 0.17/0.51 Following clause subsumed by 543 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)=c_Groups_Oone__class_Oone(tc_Int_Oint)|A!=c_Groups_Oone__class_Oone(tc_Int_Oint)|B!=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 0.17/0.51 Following clause subsumed by 808 during input processing: 0 [] {-} -class_Power_Opower(A)| -class_Rings_Osemiring__0(A)|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Power_Opower__class_Opower(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B))=c_Groups_Oone__class_Oone(A).
% 0.17/0.51 Following clause subsumed by 809 during input processing: 0 [] {-} -class_Power_Opower(A)| -class_Rings_Osemiring__0(A)|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Power_Opower__class_Opower(A,c_Groups_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,B))=c_Groups_Ozero__class_Ozero(A).
% 0.17/0.51 Following clause subsumed by 819 during input processing: 0 [] {-} -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)))|c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))|c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B).
% 0.17/0.51 Following clause subsumed by 823 during input processing: 0 [] {-} -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)))| -c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)).
% 0.17/0.51 Following clause subsumed by 822 during input processing: 0 [] {-} -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)))|c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))| -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),B).
% 0.17/0.51 Following clause subsumed by 861 during input processing: 0 [] {-} -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless__eq(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)),c_Groups_Ozero__class_Ozero(A))|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 0.17/0.51 Following clause subsumed by 862 during input processing: 0 [] {-} -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless__eq(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)),c_Groups_Ozero__class_Ozero(A))| -c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))|B=c_Groups_Ozero__class_Ozero(A).
% 0.17/0.51 Following clause subsumed by 863 during input processing: 0 [] {-} -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless__eq(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A))|c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)).
% 0.17/0.51 Following clause subsumed by 864 during input processing: 0 [] {-} -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless__eq(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A))|B=c_Groups_Ozero__class_Ozero(A).
% 0.17/0.51 Following clause subsumed by 865 during input processing: 0 [] {-} -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless__eq(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)),c_Groups_Ozero__class_Ozero(A))|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))| -c_Orderings_Oord__class_Oless__eq(A,B,c_Groups_Ozero__class_Ozero(A)).
% 0.17/0.51 Following clause subsumed by 866 during input processing: 0 [] {-} -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless__eq(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)),c_Groups_Ozero__class_Ozero(A))|c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,C))|B!=c_Groups_Ozero__class_Ozero(A).
% 0.17/0.51 Following clause subsumed by 803 during input processing: 0 [] {-} -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Power_Opower__class_Opower(A,B,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(A,C,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))| -c_Orderings_Oord__class_Oless__eq(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,B,C).
% 0.17/0.51 Following clause subsumed by 455 during input processing: 0 [] {-} A!=B|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B).
% 0.17/0.51 Following clause subsumed by 898 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A,C)|c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))| -c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B,C).
% 0.17/0.51 Following clause subsumed by 93 during input processing: 0 [] {-} c_Rings_Odvd__class_Odvd(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat))|A!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 0.17/0.51 Following clause subsumed by 918 during input processing: 0 [flip.2] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=A.
% 0.17/0.51 Following clause subsumed by 43 during input processing: 0 [] {-} A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 0.17/0.51 Following clause subsumed by 918 during input processing: 0 [flip.2] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A))|c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A),c_Groups_Oone__class_Oone(tc_Nat_Onat)))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,A).
% 0.17/0.51 Following clause subsumed by 940 during input processing: 0 [] {-} -c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,A,B),c_Power_Opower__class_Opower(tc_Int_Oint,C,B))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Rings_Odvd__class_Odvd(tc_Int_Oint,A,C).
% 0.17/0.51 Following clause subsumed by 943 during input processing: 0 [] {-} A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,B,A),c_Power_Opower__class_Opower(tc_Nat_Onat,C,A))|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,B,C).
% 0.17/0.51 Following clause subsumed by 955 during input processing: 0 [] {-} -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,c_Divides_Odiv__class_Omod(A,C,D)),D)=c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,C),D).
% 0.17/0.51 Following clause subsumed by 957 during input processing: 0 [] {-} -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,c_Divides_Odiv__class_Omod(A,B,C),D),C)=c_Divides_Odiv__class_Omod(A,c_Groups_Oplus__class_Oplus(A,B,D),C).
% 0.17/0.52 Following clause subsumed by 962 during input processing: 0 [] {-} -class_Divides_Osemiring__div(A)| -c_Rings_Odvd__class_Odvd(A,B,C)| -c_Rings_Odvd__class_Odvd(A,B,D)|c_Rings_Odvd__class_Odvd(A,B,c_Divides_Odiv__class_Omod(A,C,D)).
% 0.17/0.52 Following clause subsumed by 961 during input processing: 0 [] {-} -class_Divides_Osemiring__div(A)| -c_Rings_Odvd__class_Odvd(A,B,c_Divides_Odiv__class_Omod(A,C,D))| -c_Rings_Odvd__class_Odvd(A,B,D)|c_Rings_Odvd__class_Odvd(A,B,C).
% 0.17/0.52 Following clause subsumed by 980 during input processing: 0 [] {-} -class_Divides_Osemiring__div(A)| -c_Rings_Odvd__class_Odvd(A,B,C)|c_Divides_Odiv__class_Omod(A,C,B)=c_Groups_Ozero__class_Ozero(A).
% 0.17/0.52 Following clause subsumed by 986 during input processing: 0 [] {-} -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(A,B,C),D),C)=c_Divides_Odiv__class_Omod(A,c_Groups_Otimes__class_Otimes(A,B,D),C).
% 0.17/0.52 Following clause subsumed by 980 during input processing: 0 [] {-} -class_Divides_Osemiring__div(A)| -class_Int_Onumber(A)| -c_Rings_Odvd__class_Odvd(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C))|c_Divides_Odiv__class_Omod(A,c_Int_Onumber__class_Onumber__of(A,C),c_Int_Onumber__class_Onumber__of(A,B))=c_Groups_Ozero__class_Ozero(A).
% 0.17/0.52 Following clause subsumed by 981 during input processing: 0 [] {-} -class_Divides_Osemiring__div(A)| -class_Int_Onumber(A)|c_Rings_Odvd__class_Odvd(A,c_Int_Onumber__class_Onumber__of(A,B),c_Int_Onumber__class_Onumber__of(A,C))|c_Divides_Odiv__class_Omod(A,c_Int_Onumber__class_Onumber__of(A,C),c_Int_Onumber__class_Onumber__of(A,B))!=c_Groups_Ozero__class_Ozero(A).
% 0.17/0.52 Following clause subsumed by 994 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Divides_Odiv__class_Omod(tc_Int_Oint,B,A)).
% 0.17/0.52 Following clause subsumed by 1001 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint))|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,B,A),c_Groups_Ozero__class_Ozero(tc_Int_Oint)).
% 0.17/0.52 Following clause subsumed by 995 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,B,A),A).
% 0.17/0.52 Following clause subsumed by 1003 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)|c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,B,A)).
% 0.17/0.52 Following clause subsumed by 1072 during input processing: 0 [] {-} -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B)=A.
% 0.17/0.52 Following clause subsumed by 1082 during input processing: 0 [] {-} -c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,A)|c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 0.17/0.52 Following clause subsumed by 1094 during input processing: 0 [] {-} c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A)| -c_Orderings_Oord__class_Oless(tc_Int_Oint,A,B).
% 0.17/0.54 Following clause subsumed by 1089 during input processing: 0 [] {-} c_Divides_Odiv__class_Odiv(tc_Int_Oint,A,B)=c_Groups_Ozero__class_Ozero(tc_Int_Oint)| -c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint))| -c_Orderings_Oord__class_Oless(tc_Int_Oint,B,A).
% 0.17/0.54 Following clause subsumed by 14 during input processing: 0 [copy,13,flip.1] {-} c_Int_OBit1(A)!=c_Int_OBit0(B).
% 0.17/0.54 Following clause subsumed by 13 during input processing: 0 [copy,14,flip.1] {-} c_Int_OBit0(A)!=c_Int_OBit1(B).
% 0.17/0.54 59 back subsumes 57.
% 0.17/0.54 60 back subsumes 56.
% 0.17/0.54 288 back subsumes 64.
% 0.17/0.54 302 back subsumes 272.
% 0.17/0.54 303 back subsumes 273.
% 0.17/0.54 304 back subsumes 274.
% 0.17/0.54 320 back subsumes 319.
% 0.17/0.54 330 back subsumes 329.
% 0.17/0.54 413 back subsumes 286.
% 0.17/0.54 701 back subsumes 697.
% 0.17/0.54 793 back subsumes 791.
% 0.17/0.54 794 back subsumes 792.
% 0.17/0.54 822 back subsumes 820.
% 0.17/0.54 937 back subsumes 808.
% 0.17/0.54 1101 back subsumes 1099.
% 0.17/0.54 1213 back subsumes 1208.
% 0.17/0.54 Following clause subsumed by 765 during input processing: 0 [copy,1238,flip.1] {-} c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A),A)!=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 0.17/0.54
% 0.17/0.54 ------------> process sos:
% 0.17/0.54 Following clause subsumed by 1381 during input processing: 0 [] {-} c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(A),B)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Nat_OSuc(B)).
% 0.17/0.54 Following clause subsumed by 1405 during input processing: 0 [] {-} c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))|c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,A)|c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,B).
% 0.17/0.54 Following clause subsumed by 1405 during input processing: 0 [] {-} c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))|c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,A)|c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,B).
% 0.17/0.54 Following clause subsumed by 1375 during input processing: 0 [demod,1412] {-} c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),A)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))).
% 0.17/0.54 Following clause subsumed by 1442 during input processing: 0 [demod,1437] {-} A=A.
% 0.17/0.54 Following clause subsumed by 1449 during input processing: 0 [demod,1337,1337] {-} A=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),A).
% 0.17/0.54 Following clause subsumed by 1442 during input processing: 0 [demod,1349,1349,1349] {-} c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B).
% 0.17/0.54 Following clause subsumed by 1455 during input processing: 0 [] {-} c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,A)|c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,B)|c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B)).
% 0.17/0.54 Following clause subsumed by 1483 during input processing: 0 [] {-} A=B|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).
% 0.17/0.54 Following clause subsumed by 1483 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A=B|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A)|hBOOL(hAPP(hAPP(C,B),A)).
% 0.17/0.54 Following clause subsumed by 1482 during input processing: 0 [demod,1337] {-} c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),A).
% 0.17/0.54 Following clause subsumed by 1442 during input processing: 0 [demod,1447,1447,1499,1440] {-} c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A))=c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A)).
% 0.17/0.54 Following clause subsumed by 1558 during input processing: 0 [] {-} c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OPls).
% 0.17/0.54 Following clause subsumed by 1534 during input processing: 0 [demod,1352,1349] {-} c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls).
% 0.17/0.54 Following clause subsumed by 1442 during input processing: 0 [demod,1567,1440,1440,1349] {-} c_Groups_Oone__class_Oone(tc_Int_Oint)=c_Groups_Oone__class_Oone(tc_Int_Oint).
% 0.37/0.57 Following clause subsumed by 1375 during input processing: 0 [demod,1597,1594] {-} c_Groups_Oplus__
% 0.37/0.57 -------- PROOF --------
% 0.37/0.57 % SZS status Theorem
% 0.37/0.57 % SZS output start Refutation
% 0.37/0.57 class_Oplus(tc_Nat_Onat,A,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),A).
% 0.37/0.57 Following clause subsumed by 1442 during input processing: 0 [demod,1567,1440,1440,1594] {-} c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 0.37/0.57 Following clause subsumed by 1442 during input processing: 0 [demod,1594,1567,1440,1440] {-} c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 0.37/0.57 Following clause subsumed by 1580 during input processing: 0 [demod,1352,1352] {-} c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls).
% 0.37/0.57 Following clause subsumed by 1442 during input processing: 0 [demod,1632] {-} c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),C)=c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B),C).
% 0.37/0.57 Following clause subsumed by 1374 during input processing: 0 [demod,1352,1352,1352] {-} hBOOL(hAPP(A,c_Divides_Odiv__class_Omod(tc_Int_Oint,B,C)))|C=c_Int_OPls|c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,C)|c_Orderings_Oord__class_Oless(tc_Int_Oint,C,c_Int_OPls).
% 0.37/0.57 Following clause subsumed by 1675 during input processing: 0 [flip.2] {-} c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B),B)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,B).
% 0.37/0.57 Following clause subsumed by 1704 during input processing: 0 [demod,1337,1597,1397,1597,1337,1597,1397] {-} c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,A)|c_Divides_Odiv__class_Omod(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint))))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 0.37/0.57 Following clause subsumed by 1442 during input processing: 0 [] {-} A=A.
% 0.37/0.57 Following clause subsumed by 1324 during input processing: 0 [copy,1324,flip.1] {-} c_Groups_Otimes__class_Otimes(tc_Int_Oint,A,B)=c_Groups_Otimes__class_Otimes(tc_Int_Oint,B,A).
% 0.37/0.57 Following clause subsumed by 1442 during input processing: 0 [copy,1339,flip.1] {-} c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls).
% 0.37/0.57 Following clause subsumed by 1442 during input processing: 0 [copy,1354,flip.1] {-} c_Int_OPls=c_Int_OPls.
% 0.37/0.57 Following clause subsumed by 1355 during input processing: 0 [copy,1355,flip.1] {-} c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,A).
% 0.37/0.57
% 0.37/0.57 ----> UNIT CONFLICT at 0.12 sec ----> 2184 [binary,2183.1,2181.1] {-} $F.
% 0.37/0.57
% 0.37/0.57 Length of proof is 11. Level of proof is 5.
% 0.37/0.57
% 0.37/0.57 ---------------- PROOF ----------------
% 0.37/0.57 % SZS status Theorem
% 0.37/0.57 % SZS output start Refutation
% 0.37/0.57
% 0.37/0.57 1115 [] {-} v_na____!=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),A)|v_thesis____.
% 0.37/0.57 1116 [copy,1115,flip.1] {-} c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),A)!=v_na____|v_thesis____.
% 0.37/0.57 1117 [] {-} -v_thesis____.
% 0.37/0.57 1318 [] {-} v_na____=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),$c1).
% 0.37/0.57 1319 [copy,1318,flip.1] {-} c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),$c1)=v_na____.
% 0.37/0.57 1335 [] {-} c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 0.37/0.57 1337,1336 [copy,1335,flip.1] {-} c_Groups_Ozero__class_Ozero(tc_Nat_Onat)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls).
% 0.37/0.57 1350 [] {-} c_Int_OPls=c_Groups_Ozero__class_Ozero(tc_Int_Oint).
% 0.37/0.57 1352,1351 [copy,1350,flip.1] {-} c_Groups_Ozero__class_Ozero(tc_Int_Oint)=c_Int_OPls.
% 0.37/0.57 1401,1400 [] {-} c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C)).
% 0.37/0.57 1415 [] {-} c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls))=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 0.37/0.57 1417,1416 [copy,1415,demod,1337,flip.1] {-} c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)).
% 0.37/0.57 1434,1433 [] {-} c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B),C)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,C)).
% 0.37/0.57 1438 [] {-} c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Ozero__class_Ozero(tc_Int_Oint))=A.
% 0.37/0.57 1440,1439 [copy,1438,demod,1352] {-} c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Int_OPls)=A.
% 0.37/0.57 1447,1446 [] {-} c_Int_OBit0(A)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A).
% 0.37/0.57 1565 [] {-} c_Int_OBit1(A)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A),A).
% 0.37/0.57 1567,1566 [copy,1565,demod,1434] {-} c_Int_OBit1(A)=c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A)).
% 0.37/0.57 1592 [] {-} c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 0.37/0.57 1594,1593 [copy,1592,demod,1337,1417,1567,1440,1440] {-} c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)).
% 0.37/0.57 1604 [] {-} c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))=c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))).
% 0.37/0.57 1606,1605 [copy,1604,demod,1594,1594,1567,1440,1440,1447,flip.1] {-} c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint))).
% 0.37/0.57 2181 [back_demod,1319,demod,1567,1440,1440,1447,1606,1401] {-} c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),$c1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),$c1))=v_na____.
% 0.37/0.57 2183 [back_demod,1116,demod,1567,1440,1440,1447,1606,1401,unit_del,1117] {-} c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),A),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),A))!=v_na____.
% 0.37/0.57 2184 [binary,2183.1,2181.1] {-} $F.
% 0.37/0.57
% 0.37/0.57 % SZS output end Refutation
% 0.37/0.57 ------------ end of proof -------------
% 0.37/0.57
% 0.37/0.57
% 0.37/0.57 Search stopped by max_proofs option.
% 0.37/0.57
% 0.37/0.57
% 0.37/0.57 Search stopped by max_proofs option.
% 0.37/0.57
% 0.37/0.57 ============ end of search ============
% 0.37/0.57
% 0.37/0.57 That finishes the proof of the theorem.
% 0.37/0.57
% 0.37/0.57 Process 8808 finished Mon Jun 6 02:00:19 2022
%------------------------------------------------------------------------------