TSTP Solution File: ALG431-1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ALG431-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n009.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 : 300s
% DateTime : Wed Aug 30 16:07:44 EDT 2023
% Result : Unsatisfiable 35.57s 35.64s
% Output : CNFRefutation 35.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 118
% Syntax : Number of formulae : 146 ( 13 unt; 103 typ; 0 def)
% Number of atoms : 78 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 74 ( 39 ~; 35 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 155 ( 98 >; 57 *; 0 +; 0 <<)
% Number of predicates : 71 ( 69 usr; 2 prp; 0-5 aty)
% Number of functors : 34 ( 34 usr; 4 con; 0-4 aty)
% Number of variables : 55 ( 7 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
class_Divides_Osemiring__div: $i > $o ).
tff(decl_23,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
tff(decl_24,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_25,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_26,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(decl_27,type,
c_Polynomial_Odegree: ( $i * $i ) > $i ).
tff(decl_28,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_29,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_30,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_32,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(decl_33,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_34,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
tff(decl_36,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(decl_37,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
tff(decl_39,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_41,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_42,type,
c_Polynomial_Opos__poly: ( $i * $i ) > $o ).
tff(decl_43,type,
c_Suc: $i > $i ).
tff(decl_44,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(decl_45,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_46,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(decl_47,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_48,type,
c_Ring__and__Field_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(decl_49,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_50,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_51,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_52,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(decl_53,type,
c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_54,type,
c_Divides_Odiv__class_Odiv: ( $i * $i * $i ) > $i ).
tff(decl_55,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(decl_56,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(decl_57,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_58,type,
c_HOL_Osgn__class_Osgn: ( $i * $i ) > $i ).
tff(decl_59,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(decl_60,type,
class_RealVector_Oreal__vector: $i > $o ).
tff(decl_61,type,
c_RealVector_OscaleR__class_OscaleR: ( $i * $i * $i ) > $i ).
tff(decl_62,type,
c_Polynomial_Ocoeff: ( $i * $i * $i ) > $i ).
tff(decl_63,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_64,type,
c_Polynomial_Opdivmod__rel: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_65,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_66,type,
c_Polynomial_Opdivmod: ( $i * $i * $i ) > $i ).
tff(decl_67,type,
class_Ring__and__Field_Osgn__if: $i > $o ).
tff(decl_68,type,
tc_nat: $i ).
tff(decl_69,type,
class_Ring__and__Field_Odvd: $i > $o ).
tff(decl_70,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
tff(decl_71,type,
class_Divides_Oring__div: $i > $o ).
tff(decl_72,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(decl_73,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_74,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(decl_75,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_76,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
tff(decl_77,type,
class_HOL_Ozero: $i > $o ).
tff(decl_78,type,
class_HOL_Oeq: $i > $o ).
tff(decl_79,type,
c_HOL_Oeq__class_Oeq: ( $i * $i * $i ) > $o ).
tff(decl_80,type,
c_Polynomial_Omonom: ( $i * $i * $i ) > $i ).
tff(decl_81,type,
c_Polynomial_Opoly__gcd: ( $i * $i * $i ) > $i ).
tff(decl_82,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
tff(decl_83,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_84,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_85,type,
class_Ring__and__Field_Oabs__if: $i > $o ).
tff(decl_86,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
tff(decl_87,type,
c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).
tff(decl_88,type,
c_Polynomial_Opoly: ( $i * $i * $i ) > $i ).
tff(decl_89,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: ( $i * $i * $i ) > $i ).
tff(decl_90,type,
class_SEQ_Obanach: $i > $o ).
tff(decl_91,type,
c_Transcendental_Oexp: ( $i * $i ) > $i ).
tff(decl_92,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(decl_93,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(decl_94,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_95,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_96,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(decl_97,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(decl_98,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(decl_99,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_100,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_101,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(decl_102,type,
class_RealVector_Oreal__algebra: $i > $o ).
tff(decl_103,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff(decl_104,type,
class_RealVector_Oreal__field: $i > $o ).
tff(decl_105,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(decl_106,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(decl_107,type,
t_a: $i ).
tff(decl_108,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_109,type,
v_p: $i ).
tff(decl_110,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
tff(decl_111,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(decl_112,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(decl_113,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(decl_114,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_115,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_116,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_117,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(decl_118,type,
c_OrderedGroup_Olordered__ab__group__add__class_Opprt: ( $i * $i ) > $i ).
tff(decl_119,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(decl_120,type,
c_Polynomial_Osynthetic__divmod: ( $i * $i * $i ) > $i ).
tff(decl_121,type,
v_thesis____: $o ).
tff(decl_122,type,
class_OrderedGroup_Ocancel__comm__monoid__add: $i > $o ).
tff(decl_123,type,
tc_RealDef_Oreal: $i ).
tff(decl_124,type,
tc_prod: ( $i * $i ) > $i ).
cnf(cls_eq__iff__diff__eq__0_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
cnf(clsrel_Ring__and__Field_Oidom_OrderedGroup_Oab__group__add,axiom,
( class_OrderedGroup_Oab__group__add(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_OrderedGroup_Oab__group__add) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oidom,axiom,
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).
cnf(tfree_tcs_01,negated_conjecture,
class_Ring__and__Field_Oidom(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs_01) ).
cnf(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Ocomm__semiring__1,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_Ring__and__Field_Ocomm__semiring__1) ).
cnf(cls_smult__diff__right_0,axiom,
( c_Polynomial_Osmult(X2,c_HOL_Ominus__class_Ominus(X3,X4,tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X2,X3,X1),c_Polynomial_Osmult(X2,X4,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__diff__right_0) ).
cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
cnf(cls_conjecture_1,negated_conjecture,
( v_thesis____
| v_p != c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_0,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_synthetic__div__correct_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_Polynomial_Osmult(X3,c_Polynomial_Osynthetic__div(X2,X3,X1),X1),tc_Polynomial_Opoly(X1)) = c_Polynomial_OpCons(c_Polynomial_Opoly(X2,X3,X1),c_Polynomial_Osynthetic__div(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__correct_0) ).
cnf(cls_synthetic__div__eq__0__iff_1,axiom,
( c_Polynomial_Osynthetic__div(X2,X3,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Odegree(X2,X1) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__eq__0__iff_1) ).
cnf(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Ocomm__ring,axiom,
( class_Ring__and__Field_Ocomm__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_Ring__and__Field_Ocomm__ring) ).
cnf(cls_r_0,axiom,
( c_Polynomial_Odegree(v_p,t_a) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(t_a)
| ~ class_Int_Oring__char__0(t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r_0) ).
cnf(tfree_tcs,negated_conjecture,
class_Int_Oring__char__0(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Ocomm__semiring__0,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_Ring__and__Field_Ocomm__semiring__0) ).
cnf(c_0_15,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_eq__iff__diff__eq__0_0 ).
cnf(c_0_16,axiom,
( class_OrderedGroup_Oab__group__add(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
clsrel_Ring__and__Field_Oidom_OrderedGroup_Oab__group__add ).
cnf(c_0_17,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,X2) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,axiom,
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Oidom ).
cnf(c_0_19,plain,
( c_HOL_Ominus__class_Ominus(X1,X1,tc_Polynomial_Opoly(X2)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,negated_conjecture,
class_Ring__and__Field_Oidom(t_a),
tfree_tcs_01 ).
cnf(c_0_21,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
clsrel_Ring__and__Field_Oidom_Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_22,negated_conjecture,
c_HOL_Ominus__class_Ominus(X1,X1,tc_Polynomial_Opoly(t_a)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,axiom,
( c_Polynomial_Osmult(X2,c_HOL_Ominus__class_Ominus(X3,X4,tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X2,X3,X1),c_Polynomial_Osmult(X2,X4,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
cls_smult__diff__right_0 ).
cnf(c_0_24,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I6_J_0 ).
cnf(c_0_25,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_26,negated_conjecture,
( v_thesis____
| v_p != c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a) ),
cls_conjecture_1 ).
cnf(c_0_27,negated_conjecture,
~ v_thesis____,
cls_conjecture_0 ).
cnf(c_0_28,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_Polynomial_Osmult(X3,c_Polynomial_Osynthetic__div(X2,X3,X1),X1),tc_Polynomial_Opoly(X1)) = c_Polynomial_OpCons(c_Polynomial_Opoly(X2,X3,X1),c_Polynomial_Osynthetic__div(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_synthetic__div__correct_0 ).
cnf(c_0_29,axiom,
( c_Polynomial_Osynthetic__div(X2,X3,X1) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| c_Polynomial_Odegree(X2,X1) != c_HOL_Ozero__class_Ozero(tc_nat) ),
cls_synthetic__div__eq__0__iff_1 ).
cnf(c_0_30,negated_conjecture,
( c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| ~ class_Ring__and__Field_Ocomm__ring(t_a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_22]) ).
cnf(c_0_31,axiom,
( class_Ring__and__Field_Ocomm__ring(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
clsrel_Ring__and__Field_Oidom_Ring__and__Field_Ocomm__ring ).
cnf(c_0_32,plain,
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = X1
| ~ class_Ring__and__Field_Oidom(X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,axiom,
( c_Polynomial_Odegree(v_p,t_a) = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(t_a)
| ~ class_Int_Oring__char__0(t_a) ),
cls_r_0 ).
cnf(c_0_34,negated_conjecture,
class_Int_Oring__char__0(t_a),
tfree_tcs ).
cnf(c_0_35,negated_conjecture,
c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a) != v_p,
inference(sr,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_36,plain,
( c_Polynomial_OpCons(c_Polynomial_Opoly(X1,X2,X3),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3) = c_HOL_Oplus__class_Oplus(X1,c_Polynomial_Osmult(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)),X3),tc_Polynomial_Opoly(X3))
| c_Polynomial_Odegree(X1,X3) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_37,negated_conjecture,
c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_20])]) ).
cnf(c_0_38,negated_conjecture,
c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),tc_Polynomial_Opoly(t_a)) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_20]) ).
cnf(c_0_39,plain,
c_Polynomial_Odegree(v_p,t_a) = c_HOL_Ozero__class_Ozero(tc_nat),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_20]),c_0_34])]) ).
cnf(c_0_40,negated_conjecture,
~ class_Ring__and__Field_Ocomm__semiring__0(t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38])]),c_0_39])]) ).
cnf(c_0_41,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
clsrel_Ring__and__Field_Oidom_Ring__and__Field_Ocomm__semiring__0 ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ALG431-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 05:54:35 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.55/0.58 start to proof: theBenchmark
% 35.57/35.64 % Version : CSE_E---1.5
% 35.57/35.64 % Problem : theBenchmark.p
% 35.57/35.64 % Proof found
% 35.57/35.64 % SZS status Theorem for theBenchmark.p
% 35.57/35.64 % SZS output start Proof
% See solution above
% 35.57/35.64 % Total time : 35.029000 s
% 35.57/35.64 % SZS output end Proof
% 35.57/35.64 % Total time : 35.054000 s
%------------------------------------------------------------------------------