TSTP Solution File: SWW186+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW186+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n015.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 : Fri Sep 1 00:16:24 EDT 2023
% Result : Theorem 1.15s 1.30s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 138
% Syntax : Number of formulae : 168 ( 12 unt; 128 typ; 0 def)
% Number of atoms : 83 ( 52 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 76 ( 33 ~; 29 |; 5 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 199 ( 121 >; 78 *; 0 +; 0 <<)
% Number of predicates : 77 ( 75 usr; 1 prp; 0-5 aty)
% Number of functors : 53 ( 53 usr; 7 con; 0-5 aty)
% Number of variables : 48 ( 7 sgn; 26 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
tff(decl_24,type,
tc_Polynomial_Opoly: $i > $i ).
tff(decl_25,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_26,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: ( $i * $i * $i ) > $i ).
tff(decl_27,type,
c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_31,type,
class_Rings_Oidom: $i > $o ).
tff(decl_32,type,
class_Groups_Ozero: $i > $o ).
tff(decl_33,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_34,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_35,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_36,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_37,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_38,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_39,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_40,type,
c_Polynomial_Opoly__rec: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_41,type,
c_fequal: ( $i * $i ) > $i ).
tff(decl_42,type,
c_If: ( $i * $i * $i * $i ) > $i ).
tff(decl_43,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(decl_44,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_45,type,
c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_47,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_48,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_49,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_50,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_51,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_52,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_53,type,
c_Polynomial_Opoly: ( $i * $i ) > $i ).
tff(decl_54,type,
class_Fields_Ofield: $i > $o ).
tff(decl_55,type,
c_Polynomial_Opdivmod__rel: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_56,type,
class_Lattices_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_57,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_58,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_59,type,
c_Rings_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).
tff(decl_60,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_61,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_62,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_63,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_64,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(decl_65,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(decl_66,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_67,type,
class_Rings_Odvd: $i > $o ).
tff(decl_68,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_69,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_70,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_71,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_72,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_73,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_74,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(decl_75,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(decl_76,type,
class_Rings_Osemiring__0: $i > $o ).
tff(decl_77,type,
hBOOL: $i > $o ).
tff(decl_78,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_79,type,
c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).
tff(decl_80,type,
c_Polynomial_Opos__poly: ( $i * $i ) > $o ).
tff(decl_81,type,
c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).
tff(decl_82,type,
tc_Nat_Onat: $i ).
tff(decl_83,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_84,type,
class_Orderings_Oord: $i > $o ).
tff(decl_85,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_86,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_87,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff(decl_88,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_89,type,
c_Polynomial_Odegree: ( $i * $i ) > $i ).
tff(decl_90,type,
c_Polynomial_Omonom: ( $i * $i * $i ) > $i ).
tff(decl_91,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(decl_92,type,
class_Groups_Oone: $i > $o ).
tff(decl_93,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_94,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_95,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_96,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(decl_97,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_98,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_99,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_100,type,
class_Groups_Ouminus: $i > $o ).
tff(decl_101,type,
class_Rings_Ocomm__ring: $i > $o ).
tff(decl_102,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_103,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_104,type,
class_Rings_Oring: $i > $o ).
tff(decl_105,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_106,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(decl_107,type,
c_Polynomial_Ocoeff: ( $i * $i ) > $i ).
tff(decl_108,type,
tc_Int_Oint: $i ).
tff(decl_109,type,
class_Power_Opower: $i > $o ).
tff(decl_110,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_111,type,
c_Nat_OSuc: $i > $i ).
tff(decl_112,type,
c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).
tff(decl_113,type,
c_Polynomial_Opoly__gcd: ( $i * $i * $i ) > $i ).
tff(decl_114,type,
c_Rings_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(decl_115,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
tff(decl_116,type,
class_Rings_Odivision__ring: $i > $o ).
tff(decl_117,type,
class_Fields_Olinordered__field: $i > $o ).
tff(decl_118,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
tff(decl_119,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
tff(decl_120,type,
c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).
tff(decl_121,type,
class_Divides_Osemiring__div: $i > $o ).
tff(decl_122,type,
class_Divides_Oring__div: $i > $o ).
tff(decl_123,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_124,type,
class_Groups_Ominus: $i > $o ).
tff(decl_125,type,
class_Groups_Oplus: $i > $o ).
tff(decl_126,type,
class_Groups_Ocancel__comm__monoid__add: $i > $o ).
tff(decl_127,type,
tc_HOL_Obool: $i ).
tff(decl_128,type,
t_a: $i ).
tff(decl_129,type,
v_p: $i ).
tff(decl_130,type,
v_h: $i ).
tff(decl_131,type,
v_a: $i ).
tff(decl_132,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_133,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_134,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_135,type,
esk4_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_136,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_137,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_138,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_139,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_140,type,
esk9_1: $i > $i ).
tff(decl_141,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_142,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_143,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_144,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_145,type,
esk14_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_146,type,
esk15_3: ( $i * $i * $i ) > $i ).
tff(decl_147,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_148,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_149,type,
esk18_2: ( $i * $i ) > $i ).
fof(fact_offset__poly__eq__0__lemma,axiom,
! [X6,X7,X8,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),c_Polynomial_Osmult(X5,X8,X7),c_Polynomial_OpCons(X5,X6,X7)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))
=> X7 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__eq__0__lemma) ).
fof(conj_0,hypothesis,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
=> v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(conj_1,hypothesis,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(tfree_0,hypothesis,
class_Rings_Ocomm__semiring__0(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_0) ).
fof(fact_smult__0__right,axiom,
! [X6,X5] :
( class_Rings_Ocomm__semiring__0(X5)
=> c_Polynomial_Osmult(X5,X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__right) ).
fof(fact_add__poly__code_I1_J,axiom,
! [X10,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5)),X10) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).
fof(clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add,axiom,
! [X87] :
( class_Rings_Ocomm__semiring__0(X87)
=> class_Groups_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add) ).
fof(fact_pCons__eq__0__iff,axiom,
! [X11,X12,X13] :
( class_Groups_Ozero(X13)
=> ( c_Polynomial_OpCons(X13,X12,X11) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X13))
<=> ( X12 = c_Groups_Ozero__class_Ozero(X13)
& X11 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X13)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).
fof(clrel_Rings_Ocomm__semiring__0__Groups_Ozero,axiom,
! [X87] :
( class_Rings_Ocomm__semiring__0(X87)
=> class_Groups_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clrel_Rings_Ocomm__semiring__0__Groups_Ozero) ).
fof(conj_2,conjecture,
( v_a = c_Groups_Ozero__class_Ozero(t_a)
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
fof(c_0_10,plain,
! [X102,X103,X104,X105] :
( ~ class_Rings_Ocomm__semiring__0(X105)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X105),c_Polynomial_Osmult(X105,X104,X103),c_Polynomial_OpCons(X105,X102,X103)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X105))
| X103 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X105)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__eq__0__lemma])]) ).
fof(c_0_11,hypothesis,
( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(fof_nnf,[status(thm)],[conj_0]) ).
cnf(c_0_12,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),c_Polynomial_OpCons(X1,X4,X3)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,hypothesis,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(split_conjunct,[status(thm)],[conj_1]) ).
cnf(c_0_14,hypothesis,
class_Rings_Ocomm__semiring__0(t_a),
inference(split_conjunct,[status(thm)],[tfree_0]) ).
fof(c_0_15,plain,
! [X136,X137] :
( ~ class_Rings_Ocomm__semiring__0(X137)
| c_Polynomial_Osmult(X137,X136,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X137))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X137)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__0__right])]) ).
cnf(c_0_16,hypothesis,
( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,hypothesis,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).
fof(c_0_18,plain,
! [X132,X133] :
( ~ class_Groups_Ocomm__monoid__add(X133)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X133),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X133)),X132) = X132 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__poly__code_I1_J])]) ).
fof(c_0_19,plain,
! [X3003] :
( ~ class_Rings_Ocomm__semiring__0(X3003)
| class_Groups_Ocomm__monoid__add(X3003) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add])]) ).
fof(c_0_20,plain,
! [X125,X126,X127] :
( ( X126 = c_Groups_Ozero__class_Ozero(X127)
| c_Polynomial_OpCons(X127,X126,X125) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X127))
| ~ class_Groups_Ozero(X127) )
& ( X125 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X127))
| c_Polynomial_OpCons(X127,X126,X125) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X127))
| ~ class_Groups_Ozero(X127) )
& ( X126 != c_Groups_Ozero__class_Ozero(X127)
| X125 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X127))
| c_Polynomial_OpCons(X127,X126,X125) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X127))
| ~ class_Groups_Ozero(X127) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__eq__0__iff])])]) ).
fof(c_0_21,plain,
! [X3009] :
( ~ class_Rings_Ocomm__semiring__0(X3009)
| class_Groups_Ozero(X3009) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[clrel_Rings_Ocomm__semiring__0__Groups_Ozero])]) ).
cnf(c_0_22,plain,
( c_Polynomial_Osmult(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,hypothesis,
c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = v_p,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17])]) ).
cnf(c_0_24,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( class_Groups_Ocomm__monoid__add(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_26,negated_conjecture,
~ ( v_a = c_Groups_Ozero__class_Ozero(t_a)
& v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(assume_negation,[status(cth)],[conj_2]) ).
cnf(c_0_27,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Polynomial_OpCons(X2,X1,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Groups_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
( class_Groups_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,hypothesis,
c_Polynomial_Osmult(t_a,X1,v_p) = v_p,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_14])]) ).
cnf(c_0_30,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = X2
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_31,negated_conjecture,
( v_a != c_Groups_Ozero__class_Ozero(t_a)
| v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(fof_nnf,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Polynomial_OpCons(X2,X1,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,hypothesis,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),v_p,c_Polynomial_OpCons(t_a,v_a,v_p)) = v_p,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_17]),c_0_23]),c_0_17]),c_0_23]),c_0_23]),c_0_29]) ).
cnf(c_0_34,hypothesis,
c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),v_p,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_23]),c_0_14])]) ).
cnf(c_0_35,negated_conjecture,
( v_a != c_Groups_Ozero__class_Ozero(t_a)
| v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,hypothesis,
( X1 = c_Groups_Ozero__class_Ozero(t_a)
| c_Polynomial_OpCons(t_a,X1,X2) != v_p ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_14]),c_0_23]) ).
cnf(c_0_37,hypothesis,
c_Polynomial_OpCons(t_a,v_a,v_p) = v_p,
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
c_Groups_Ozero__class_Ozero(t_a) != v_a,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_23])]) ).
cnf(c_0_39,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW186+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 21:23:39 EDT 2023
% 0.19/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 1.15/1.30 % Version : CSE_E---1.5
% 1.15/1.30 % Problem : theBenchmark.p
% 1.15/1.30 % Proof found
% 1.15/1.30 % SZS status Theorem for theBenchmark.p
% 1.15/1.30 % SZS output start Proof
% See solution above
% 1.24/1.31 % Total time : 0.670000 s
% 1.24/1.31 % SZS output end Proof
% 1.24/1.31 % Total time : 0.710000 s
%------------------------------------------------------------------------------