TSTP Solution File: ALG396-1 by SOS---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SOS---2.0
% Problem : ALG396-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : sos-script %s
% Computer : n027.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 14 18:01:48 EDT 2022
% Result : Unsatisfiable 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ALG396-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : sos-script %s
% 0.12/0.33 % Computer : n027.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 : Tue Jun 7 22:21:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.44 ----- Otter 3.2, August 2001 -----
% 0.18/0.44 The process was started by sandbox2 on n027.cluster.edu,
% 0.18/0.44 Tue Jun 7 22:21:11 2022
% 0.18/0.44 The command was "./sos". The process ID is 14630.
% 0.18/0.44
% 0.18/0.44 set(prolog_style_variables).
% 0.18/0.44 set(auto).
% 0.18/0.44 dependent: set(auto1).
% 0.18/0.44 dependent: set(process_input).
% 0.18/0.44 dependent: clear(print_kept).
% 0.18/0.44 dependent: clear(print_new_demod).
% 0.18/0.44 dependent: clear(print_back_demod).
% 0.18/0.44 dependent: clear(print_back_sub).
% 0.18/0.44 dependent: set(control_memory).
% 0.18/0.44 dependent: assign(max_mem, 12000).
% 0.18/0.44 dependent: assign(pick_given_ratio, 4).
% 0.18/0.44 dependent: assign(stats_level, 1).
% 0.18/0.44 dependent: assign(pick_semantic_ratio, 3).
% 0.18/0.44 dependent: assign(sos_limit, 5000).
% 0.18/0.44 dependent: assign(max_weight, 60).
% 0.18/0.44 clear(print_given).
% 0.18/0.44
% 0.18/0.44 list(usable).
% 0.18/0.44
% 0.18/0.44 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 0.18/0.44
% 0.18/0.44 This ia a non-Horn set with equality. The strategy will be
% 0.18/0.44 Knuth-Bendix, ordered hyper_res, ur_res, factoring, and
% 0.18/0.44 unit deletion, with positive clauses in sos and nonpositive
% 0.18/0.44 clauses in usable.
% 0.18/0.44
% 0.18/0.44 dependent: set(knuth_bendix).
% 0.18/0.44 dependent: set(para_from).
% 0.18/0.44 dependent: set(para_into).
% 0.18/0.44 dependent: clear(para_from_right).
% 0.18/0.44 dependent: clear(para_into_right).
% 0.18/0.44 dependent: set(para_from_vars).
% 0.18/0.44 dependent: set(eq_units_both_ways).
% 0.18/0.44 dependent: set(dynamic_demod_all).
% 0.18/0.44 dependent: set(dynamic_demod).
% 0.18/0.44 dependent: set(order_eq).
% 0.18/0.44 dependent: set(back_demod).
% 0.18/0.44 dependent: set(lrpo).
% 0.18/0.44 dependent: set(hyper_res).
% 0.18/0.44 dependent: set(unit_deletion).
% 0.18/0.44 dependent: set(factor).
% 0.18/0.44
% 0.18/0.44 ------------> process usable:
% 0.18/0.44 Following clause subsumed by 30 during input processing: 0 [] {-} -class_Orderings_Oorder(A)|B=C|c_HOL_Oord__class_Oless(B,C,A)| -c_lessequals(B,C,A).
% 0.18/0.44 Following clause subsumed by 30 during input processing: 0 [] {-} -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)|B=C| -c_lessequals(B,C,A).
% 0.18/0.44 Following clause subsumed by 30 during input processing: 0 [] {-} -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_lessequals(B,C,A)|B=C.
% 0.18/0.44 Following clause subsumed by 31 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(B,C,A)| -c_lessequals(B,C,A).
% 0.18/0.44 Following clause subsumed by 32 during input processing: 0 [] {-} -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)|C=B| -c_lessequals(B,C,A).
% 0.18/0.44 Following clause subsumed by 36 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).
% 0.18/0.44 Following clause subsumed by 44 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).
% 0.18/0.44 Following clause subsumed by 44 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).
% 0.18/0.44 Following clause subsumed by 47 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).
% 0.18/0.44 Following clause subsumed by 48 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).
% 0.18/0.44 Following clause subsumed by 63 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(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 0.18/0.44 Following clause subsumed by 98 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).
% 0.18/0.44 Following clause subsumed by 98 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).
% 0.18/0.44 Following clause subsumed by 99 during input processing: 0 [] {-} -class_Orderings_Oorder(A)|B=C| -c_lessequals(C,B,A)| -c_lessequals(B,C,A).
% 0.18/0.44 Following clause subsumed by 98 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.
% 0.18/0.44 Following clause subsumed by 99 during input processing: 0 [] {-} -class_Orderings_Oorder(A)|B=C| -c_lessequals(C,B,A)| -c_lessequals(B,C,A).
% 0.18/0.44 Following clause subsumed by 104 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.
% 0.18/0.44 Following clause subsumed by 104 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).
% 0.18/0.44 Following clause subsumed by 104 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).
% 0.18/0.44 Following clause subsumed by 45 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).
% 0.18/0.44 Following clause subsumed by 44 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).
% 0.18/0.44 Following clause subsumed by 130 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).
% 0.18/0.44 Following clause subsumed by 46 during input processing: 0 [flip.2] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,D,A),C,A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A).
% 0.18/0.44 Following clause subsumed by 157 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).
% 0.18/0.44 Following clause subsumed by 159 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).
% 0.18/0.44 Following clause subsumed by 182 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).
% 0.18/0.44 Following clause subsumed by 181 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).
% 0.18/0.44 Following clause subsumed by 191 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).
% 0.18/0.45 Following clause subsumed by 208 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).
% 0.18/0.45 Following clause subsumed by 217 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).
% 0.18/0.45 Following clause subsumed by 218 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).
% 0.18/0.45 Following clause subsumed by 218 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).
% 0.18/0.45 Following clause subsumed by 234 during input processing: 0 [flip.2] {-} -class_RealVector_Oreal__normed__algebra(A)|c_RealVector_OscaleR__class_OscaleR(B,c_HOL_Otimes__class_Otimes(C,D,A),A)=c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(B,C,A),D,A).
% 0.18/0.45 Following clause subsumed by 236 during input processing: 0 [flip.2] {-} -class_RealVector_Oreal__normed__algebra(A)|c_RealVector_OscaleR__class_OscaleR(C,c_HOL_Otimes__class_Otimes(B,D,A),A)=c_HOL_Otimes__class_Otimes(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A).
% 0.18/0.45 Following clause subsumed by 145 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).
% 0.18/0.45 Following clause subsumed by 146 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).
% 0.18/0.45 Following clause subsumed by 252 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).
% 0.18/0.45 Following clause subsumed by 253 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).
% 0.18/0.45 Following clause subsumed by 269 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_lessequals(c_Orderings_Oord__class_Omax(B,C,A),D,A)| -c_lessequals(C,D,A)| -c_lessequals(B,D,A).
% 0.18/0.45 Following clause subsumed by 269 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_lessequals(c_Orderings_Oord__class_Omax(B,C,A),D,A)| -c_lessequals(C,D,A)| -c_lessequals(B,D,A).
% 0.18/0.45 Following clause subsumed by 281 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,A),A)| -c_lessequals(B,D,A)| -c_lessequals(B,C,A).
% 0.18/0.45 Following clause subsumed by 281 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,A),A)| -c_lessequals(B,D,A)| -c_lessequals(B,C,A).
% 0.18/0.45 Following clause subsumed by 294 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).
% 0.18/0.45 Following clause subsumed by 300 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).
% 0.18/0.45 Following clause subsumed by 310 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).
% 0.18/0.45 Following clause subsumed by 310 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).
% 0.18/0.45 Following clause subsumed by 318 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,B,A)|c_lessequals(B,B,A).
% 0.18/0.45 Following clause subsumed by 318 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_lessequals(B,C,A)|c_HOL_Oord__class_Oless(C,B,A).
% 0.18/0.45 Following clause subsumed by 318 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_lessequals(C,B,A).
% 0.18/0.45 Following clause subsumed by 320 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)| -c_lessequals(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 0.18/0.45 Following clause subsumed by 22 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).
% 0.18/0.45 Following clause subsumed by 23 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).
% 0.18/0.45 Following clause subsumed by 272 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).
% 0.18/0.45 Following clause subsumed by 361 during input processing: 0 [] {-} -class_RealVector_Oreal__normed__vector(A)|c_RealVector_OscaleR__class_OscaleR(B,c_RealVector_OscaleR__class_OscaleR(C,D,A),A)=c_RealVector_OscaleR__class_OscaleR(C,c_RealVector_OscaleR__class_OscaleR(B,D,A),A).
% 0.18/0.45 Following clause subsumed by 365 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).
% 0.18/0.45 Following clause subsumed by 377 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),D,A)| -c_lessequals(B,D,A).
% 0.18/0.45 Following clause subsumed by 378 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_lessequals(c_Orderings_Oord__class_Omin(B,C,A),D,A)| -c_lessequals(C,D,A).
% 0.18/0.45 Following clause subsumed by 375 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_lessequals(B,C,A)| -c_lessequals(B,c_Orderings_Oord__class_Omin(C,D,A),A).
% 0.18/0.45 Following clause subsumed by 376 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_lessequals(B,C,A)| -c_lessequals(B,c_Orderings_Oord__class_Omin(D,C,A),A).
% 0.18/0.45 Following clause subsumed by 399 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_lessequals(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_lessequals(B,C,A).
% 0.18/0.45 Following clause subsumed by 400 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_lessequals(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_lessequals(B,D,A).
% 0.18/0.45 Following clause subsumed by 397 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_lessequals(B,C,A)| -c_lessequals(c_Orderings_Oord__class_Omax(B,D,A),C,A).
% 0.18/0.45 Following clause subsumed by 398 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_lessequals(B,C,A)| -c_lessequals(c_Orderings_Oord__class_Omax(D,B,A),C,A).
% 0.18/0.45 Following clause subsumed by 406 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.
% 0.18/0.45 Following clause subsumed by 412 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).
% 0.18/0.45 Following clause subsumed by 415 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).
% 0.18/0.45 Following clause subsumed by 416 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).
% 0.18/0.45 Following clause subsumed by 413 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).
% 0.18/0.45 Following clause subsumed by 428 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_HOL_Oord__class_Oless(B,D,A).
% 0.18/0.45 Following clause subsumed by 429 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,c_Orderings_Oord__class_Omax(C,D,A),A)| -c_HOL_Oord__class_Oless(B,C,A).
% 0.18/0.45 Following clause subsumed by 435 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).
% 0.18/0.45 Following clause subsumed by 442 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).
% 0.18/0.45 Following clause subsumed by 444 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(B,C,A),D,A)| -c_HOL_Oord__class_Oless(C,D,A).
% 0.18/0.45 Following clause subsumed by 445 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(B,C,A),D,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 0.18/0.45 Following clause subsumed by 278 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).
% 0.18/0.45 Following clause subsumed by 468 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).
% 0.18/0.45 Following clause subsumed by 471 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).
% 0.18/0.45 Following clause subsumed by 472 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).
% 0.18/0.45 Following clause subsumed by 471 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).
% 0.18/0.45 Following clause subsumed by 488 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.
% 0.18/0.45 Following clause subsumed by 502 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.
% 0.18/0.48 Following clause subsumed by 502 during input processing: 0 [flip.2] {-} -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ouminus__class_Ouminus(c_
% 0.18/0.48 -------- PROOF --------
% 0.18/0.48 % SZS status Unsatisfiable
% 0.18/0.48 % SZS output start Refutation
% 0.18/0.48 HOL_Ouminus__class_Ouminus(B,A),A)=B.
% 0.18/0.48 Following clause subsumed by 502 during input processing: 0 [] {-} -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A)=B.
% 0.18/0.48 Following clause subsumed by 506 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).
% 0.18/0.48 Following clause subsumed by 507 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).
% 0.18/0.48 Following clause subsumed by 508 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).
% 0.18/0.48 Following clause subsumed by 509 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).
% 0.18/0.48 Following clause subsumed by 537 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).
% 0.18/0.48 Following clause subsumed by 559 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).
% 0.18/0.48 Following clause subsumed by 558 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).
% 0.18/0.48 Following clause subsumed by 442 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).
% 0.18/0.48 Following clause subsumed by 395 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).
% 0.18/0.48 Following clause subsumed by 602 during input processing: 0 [] {-} -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 0.18/0.48 Following clause subsumed by 635 during input processing: 0 [] {-} -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 0.18/0.48 Following clause subsumed by 644 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).
% 0.18/0.48 Following clause subsumed by 645 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).
% 0.18/0.48 12 back subsumes 9.
% 0.18/0.48 13 back subsumes 11.
% 0.18/0.48 320 back subsumes 319.
% 0.18/0.48 441 back subsumes 207.
% 0.18/0.48 651 back subsumes 626.
% 0.18/0.48 749 back subsumes 748.
% 0.18/0.48
% 0.18/0.48 ------------> process sos:
% 0.18/0.48
% 0.18/0.48 ----> UNIT CONFLICT at 0.07 sec ----> 868 [binary,866.1,655.1] {-} $F.
% 0.18/0.48
% 0.18/0.48 Length of proof is 1. Level of proof is 1.
% 0.18/0.48
% 0.18/0.48 ---------------- PROOF ----------------
% 0.18/0.48 % SZS status Unsatisfiable
% 0.18/0.48 % SZS output start Refutation
% 0.18/0.48
% 0.18/0.48 654 [] {-} c_Polynomial_Opoly(v_pa____,v_x____,tc_Complex_Ocomplex)!=c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(v_x____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex).
% 0.18/0.48 655 [copy,654,flip.1] {-} c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(v_x____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex)!=c_Polynomial_Opoly(v_pa____,v_x____,tc_Complex_Ocomplex).
% 0.18/0.48 866 [] {-} c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(A,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex)=c_Polynomial_Opoly(v_pa____,A,tc_Complex_Ocomplex).
% 0.18/0.48 868 [binary,866.1,655.1] {-} $F.
% 0.18/0.48
% 0.18/0.48 % SZS output end Refutation
% 0.18/0.48 ------------ end of proof -------------
% 0.18/0.48
% 0.18/0.48
% 0.18/0.48 Search stopped by max_proofs option.
% 0.18/0.48
% 0.18/0.48
% 0.18/0.48 Search stopped by max_proofs option.
% 0.18/0.48
% 0.18/0.48 ============ end of search ============
% 0.18/0.48
% 0.18/0.48 That finishes the proof of the theorem.
% 0.18/0.48
% 0.18/0.48 Process 14630 finished Tue Jun 7 22:21:11 2022
%------------------------------------------------------------------------------