TSTP Solution File: ALG425-1 by SOS---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SOS---2.0
% Problem : ALG425-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : sos-script %s
% Computer : n018.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 18:01:52 EDT 2022
% Result : Unsatisfiable 0.21s 0.48s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG425-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : sos-script %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jun 8 18:52:52 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.45 ----- Otter 3.2, August 2001 -----
% 0.21/0.45 The process was started by sandbox on n018.cluster.edu,
% 0.21/0.45 Wed Jun 8 18:52:52 2022
% 0.21/0.45 The command was "./sos". The process ID is 29077.
% 0.21/0.45
% 0.21/0.45 set(prolog_style_variables).
% 0.21/0.45 set(auto).
% 0.21/0.45 dependent: set(auto1).
% 0.21/0.45 dependent: set(process_input).
% 0.21/0.45 dependent: clear(print_kept).
% 0.21/0.45 dependent: clear(print_new_demod).
% 0.21/0.45 dependent: clear(print_back_demod).
% 0.21/0.45 dependent: clear(print_back_sub).
% 0.21/0.45 dependent: set(control_memory).
% 0.21/0.45 dependent: assign(max_mem, 12000).
% 0.21/0.45 dependent: assign(pick_given_ratio, 4).
% 0.21/0.45 dependent: assign(stats_level, 1).
% 0.21/0.45 dependent: assign(pick_semantic_ratio, 3).
% 0.21/0.45 dependent: assign(sos_limit, 5000).
% 0.21/0.45 dependent: assign(max_weight, 60).
% 0.21/0.45 clear(print_given).
% 0.21/0.45
% 0.21/0.45 list(usable).
% 0.21/0.45
% 0.21/0.45 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 0.21/0.45
% 0.21/0.45 This ia a non-Horn set with equality. The strategy will be
% 0.21/0.45 Knuth-Bendix, ordered hyper_res, ur_res, factoring, and
% 0.21/0.45 unit deletion, with positive clauses in sos and nonpositive
% 0.21/0.45 clauses in usable.
% 0.21/0.45
% 0.21/0.45 dependent: set(knuth_bendix).
% 0.21/0.45 dependent: set(para_from).
% 0.21/0.45 dependent: set(para_into).
% 0.21/0.45 dependent: clear(para_from_right).
% 0.21/0.45 dependent: clear(para_into_right).
% 0.21/0.45 dependent: set(para_from_vars).
% 0.21/0.45 dependent: set(eq_units_both_ways).
% 0.21/0.45 dependent: set(dynamic_demod_all).
% 0.21/0.45 dependent: set(dynamic_demod).
% 0.21/0.45 dependent: set(order_eq).
% 0.21/0.45 dependent: set(back_demod).
% 0.21/0.45 dependent: set(lrpo).
% 0.21/0.45 dependent: set(hyper_res).
% 0.21/0.45 dependent: set(unit_deletion).
% 0.21/0.45 dependent: set(factor).
% 0.21/0.45
% 0.21/0.45 ------------> process usable:
% 0.21/0.45 Following clause subsumed by 2 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oord__class_Oless(B,c_HOL_Oinverse__class_Odivide(C,D,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,D,A),C,A).
% 0.21/0.45 Following clause subsumed by 3 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),D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(B,c_HOL_Otimes__class_Otimes(D,C,A),A).
% 0.21/0.45 Following clause subsumed by 7 during input processing: 0 [flip.1] {-} c_Suc(A)!=A.
% 0.21/0.45 Following clause subsumed by 18 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).
% 0.21/0.45 Following clause subsumed by 37 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A).
% 0.21/0.45 Following clause subsumed by 37 during input processing: 0 [] {-} -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|C=B|c_HOL_Oord__class_Oless(C,B,A).
% 0.21/0.45 Following clause subsumed by 37 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.
% 0.21/0.45 Following clause subsumed by 43 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.
% 0.21/0.45 Following clause subsumed by 43 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).
% 0.21/0.45 Following clause subsumed by 43 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).
% 0.21/0.45 Following clause subsumed by 92 during input processing: 0 [] {-} -class_Divides_Osemiring__div(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A),c_Divides_Odiv__class_Omod(B,C,A),A)=B.
% 0.21/0.45 Following clause subsumed by 105 during input processing: 0 [] {-} -class_Ring__and__Field_Ofield(A)|c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(B,C,A),D,tc_Polynomial_Opoly(A))|B=c_HOL_Ozero__class_Ozero(A)| -c_Ring__and__Field_Odvd__class_Odvd(C,D,tc_Polynomial_Opoly(A)).
% 0.21/0.45 Following clause subsumed by 108 during input processing: 0 [] {-} -class_Ring__and__Field_Ofield(A)|c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_Polynomial_Opoly(A))|D=c_HOL_Ozero__class_Ozero(A)| -c_Ring__and__Field_Odvd__class_Odvd(B,c_Polynomial_Osmult(D,C,A),tc_Polynomial_Opoly(A)).
% 0.21/0.45 Following clause subsumed by 143 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 0.21/0.45 Following clause subsumed by 142 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Odivide(B,C,A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 0.21/0.45 Following clause subsumed by 162 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).
% 0.21/0.45 Following clause subsumed by 182 during input processing: 0 [] {-} -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 0.21/0.45 Following clause subsumed by 194 during input processing: 0 [] {-} c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.21/0.45 Following clause subsumed by 28 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A),A).
% 0.21/0.45 Following clause subsumed by 199 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).
% 0.21/0.45 Following clause subsumed by 200 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).
% 0.21/0.45 Following clause subsumed by 203 during input processing: 0 [flip.1] {-} c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.21/0.45 Following clause subsumed by 208 during input processing: 0 [] {-} -class_Ring__and__Field_Ofield(A)| -class_Int_Onumber__ring(A)|c_HOL_Oinverse__class_Oinverse(B,A)=c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A).
% 0.21/0.45 Following clause subsumed by 232 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).
% 0.21/0.45 Following clause subsumed by 232 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).
% 0.21/0.45 Following clause subsumed by 239 during input processing: 0 [] {-} -class_Ring__and__Field_Ofield(A)|c_HOL_Oinverse__class_Odivide(B,B,A)=c_HOL_Oone__class_Oone(A)|B=c_HOL_Ozero__class_Ozero(A).
% 0.21/0.45 Following clause subsumed by 239 during input processing: 0 [] {-} -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Odivide(B,B,A)=c_HOL_Oone__class_Oone(A)|B=c_HOL_Ozero__class_Ozero(A).
% 0.21/0.46 Following clause subsumed by 85 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).
% 0.21/0.46 Following clause subsumed by 86 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).
% 0.21/0.46 Following clause subsumed by 250 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).
% 0.21/0.46 Following clause subsumed by 260 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).
% 0.21/0.46 Following clause subsumed by 260 during input processing: 0 [] {-} -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 0.21/0.46 Following clause subsumed by 268 during input processing: 0 [] {-} c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=c_HOL_Oplus__class_Oplus(A,C,tc_nat)|B=C.
% 0.21/0.46 Following clause subsumed by 54 during input processing: 0 [] {-} -class_Ring__and__Field_Ozero__neq__one(A)|c_HOL_Ozero__class_Ozero(A)!=c_HOL_Oone__class_Oone(A).
% 0.21/0.46 Following clause subsumed by 27 during input processing: 0 [] {-} -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Oone__class_Oone(A).
% 0.21/0.46 Following clause subsumed by 201 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).
% 0.21/0.46 Following clause subsumed by 312 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).
% 0.21/0.46 Following clause subsumed by 317 during input processing: 0 [] {-} c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Otimes__class_Otimes(A,C,tc_nat)|B=C|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.21/0.46 Following clause subsumed by 330 during input processing: 0 [] {-} c_Suc(A)!=c_Suc(B)|A=B.
% 0.21/0.46 Following clause subsumed by 346 during input processing: 0 [] {-} c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,D,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat)|B=D|A=C.
% 0.21/0.46 Following clause subsumed by 363 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oinverse__class_Oinverse(B,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 0.21/0.46 Following clause subsumed by 381 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).
% 0.21/0.46 Following clause subsumed by 384 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).
% 0.21/0.46 Following clause subsumed by 385 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).
% 0.21/0.46 Following clause subsumed by 384 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).
% 0.21/0.46 Following clause subsumed by 401 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.
% 0.21/0.46 Following clause subsumed by 411 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.
% 0.21/0.46 Following clause subsumed by 411 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.
% 0.21/0.46 Following clause subsumed by 411 during input processing: 0 [] {-} -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(B,A),A)=B.
% 0.21/0.46 Following clause subsumed by 415 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).
% 0.21/0.46 Following clause subsumed by 416 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).
% 0.21/0.46 Following clause subsumed by 428 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).
% 0.21/0.46 Following clause subsumed by 429 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).
% 0.21/0.46 Following clause subsumed by 427 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).
% 0.21/0.46 Following clause subsumed by 433 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.
% 0.21/0.46 Following clause subsumed by 444 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).
% 0.21/0.46 Following clause subsumed by 203 during input processing: 0 [] {-} c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.21/0.46 Following clause subsumed by 203 during input processing: 0 [] {-} c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 0.21/0.46 Following clause subsumed by 477 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).
% 0.21/0.46 Following clause subsumed by 484 during input processing: 0 [flip.3] {-} -class_Ring__and__Field_Ofield(A)| -class_Int_Onumber__ring(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Oinverse__class_Oinverse(C,A),A)=c_HOL_Oinverse__class_Odivide(B,C,A).
% 0.21/0.46 Following clause subsumed by 501 during input processing: 0 [] {-} -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oord__class_Oless(c_HOL_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).
% 0.21/0.46 Following clause subsumed by 500 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).
% 0.21/0.47 Following clause subsumed by 260 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).
% 0.21/0.47 Following clause subsumed by 336 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).
% 0.21/0.47 Following clause subsumed by 532 during input processing: 0 [] {-} -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 0.21/0.47 Following clause subsumed by 536 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).
% 0.21/0.47 Following clause subsumed by 538 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).
% 0.21/0.47 Following clause subsumed by 543 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).
% 0.21/0.47 Following clause subsumed by 544 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).
% 0.21/0.47 Following clause subsumed by 540 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A).
% 0.21/0.47 Following clause subsumed by 554 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).
% 0.21/0.47 Following clause subsumed by 560 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A)=B.
% 0.21/0.47 Following clause subsumed by 565 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).
% 0.21/0.47 Following clause subsumed by 568 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).
% 0.21/0.47 Following clause subsumed by 569 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).
% 0.21/0.47 Following clause subsumed by 556 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).
% 0.21/0.47 Following clause subsumed by 71 during input processing: 0 [] {-} c_Polynomial_Opoly(v_pa____,A,tc_Complex_Ocomplex)!=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)|c_Polynomial_Opoly(v_qa____,A,tc_Complex_Ocomplex)=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 0.21/0.47 Following clause subsumed by 609 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A).
% 0.21/0.48 Following clause subsumed by 609 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=c_HOL_Otimes__class_Otimes(B,c_Powe
% 0.21/0.48 -------- PROOF --------
% 0.21/0.48 % SZS status Unsatisfiable
% 0.21/0.48 % SZS output start Refutation
% 0.21/0.48 r_Opower__class_Opower(B,C,A),A).
% 0.21/0.48 Following clause subsumed by 71 during input processing: 0 [] {-} c_Polynomial_Opoly(v_pa____,A,tc_Complex_Ocomplex)!=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)|c_Ring__and__Field_Odvd__class_Odvd(v_pa____,c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)).
% 0.21/0.48 Following clause subsumed by 619 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).
% 0.21/0.48 Following clause subsumed by 619 during input processing: 0 [] {-} -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A).
% 0.21/0.48 Following clause subsumed by 620 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).
% 0.21/0.48 Following clause subsumed by 619 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).
% 0.21/0.48 Following clause subsumed by 628 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).
% 0.21/0.48 80 back subsumes 79.
% 0.21/0.48 208 back subsumes 115.
% 0.21/0.48 461 back subsumes 460.
% 0.21/0.48 480 back subsumes 479.
% 0.21/0.48 Following clause subsumed by 71 during input processing: 0 [copy,690,flip.1] {-} c_Polynomial_Opoly(v_pa____,A,tc_Complex_Ocomplex)!=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 0.21/0.48 Following clause subsumed by 629 during input processing: 0 [copy,774,flip.1] {-} c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex))!=c_HOL_Otimes__class_Otimes(v_pa____,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)).
% 0.21/0.48
% 0.21/0.48 ------------> process sos:
% 0.21/0.48 Following clause subsumed by 800 during input processing: 0 [] {-} c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat).
% 0.21/0.48 Following clause subsumed by 806 during input processing: 0 [demod,797,805,797] {-} c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),B,tc_nat),tc_nat).
% 0.21/0.48 Following clause subsumed by 806 during input processing: 0 [demod,797,797] {-} c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),B,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat).
% 0.21/0.48 Following clause subsumed by 824 during input processing: 0 [demod,797,822,797,822,793,797,822] {-} c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 0.21/0.48 Following clause subsumed by 824 during input processing: 0 [demod,797,822,797,822,822] {-} c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 0.21/0.48 Following clause subsumed by 824 during input processing: 0 [demod,797,822,826,797,822] {-} c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 0.21/0.48
% 0.21/0.48 ----> UNIT CONFLICT at 0.05 sec ----> 836 [binary,834.1,774.1] {-} $F.
% 0.21/0.48
% 0.21/0.48 Length of proof is 2. Level of proof is 1.
% 0.21/0.48
% 0.21/0.48 ---------------- PROOF ----------------
% 0.21/0.48 % SZS status Unsatisfiable
% 0.21/0.48 % SZS output start Refutation
% 0.21/0.48
% 0.21/0.48 629 [] {-} c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex))!=c_HOL_Otimes__class_Otimes(v_pa____,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex)).
% 0.21/0.48 774 [copy,629,flip.1] {-} c_HOL_Otimes__class_Otimes(v_pa____,A,tc_Polynomial_Opoly(tc_Complex_Ocomplex))!=c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)).
% 0.21/0.48 833 [] {-} c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex))=c_HOL_Otimes__class_Otimes(v_pa____,c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)).
% 0.21/0.48 834 [copy,833,flip.1] {-} c_HOL_Otimes__class_Otimes(v_pa____,c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),v_c____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))=c_Power_Opower__class_Opower(v_qa____,v_na____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)).
% 0.21/0.48 836 [binary,834.1,774.1] {-} $F.
% 0.21/0.48
% 0.21/0.48 % SZS output end Refutation
% 0.21/0.48 ------------ end of proof -------------
% 0.21/0.48
% 0.21/0.48
% 0.21/0.48 Search stopped by max_proofs option.
% 0.21/0.48
% 0.21/0.48
% 0.21/0.48 Search stopped by max_proofs option.
% 0.21/0.48
% 0.21/0.48 ============ end of search ============
% 0.21/0.48
% 0.21/0.48 That finishes the proof of the theorem.
% 0.21/0.48
% 0.21/0.48 Process 29077 finished Wed Jun 8 18:52:52 2022
%------------------------------------------------------------------------------