TSTP Solution File: SWW213+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWW213+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n016.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 00:16:33 EDT 2023

% Result   : Theorem 10.11s 10.18s
% Output   : CNFRefutation 10.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :  147
% Syntax   : Number of formulae    :  160 (   7 unt; 142 typ;   0 def)
%            Number of atoms       :   32 (  17 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   29 (  15   ~;  10   |;   0   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  219 ( 133   >;  86   *;   0   +;   0  <<)
%            Number of predicates  :   78 (  76 usr;   2 prp; 0-5 aty)
%            Number of functors    :   66 (  66 usr;   8 con; 0-5 aty)
%            Number of variables   :   28 (   1 sgn;  17   !;   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_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).

tff(decl_26,type,
    c_Polynomial_Opoly: ( $i * $i ) > $i ).

tff(decl_27,type,
    c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: ( $i * $i * $i ) > $i ).

tff(decl_28,type,
    class_Int_Oring__char__0: $i > $o ).

tff(decl_29,type,
    class_Rings_Oidom: $i > $o ).

tff(decl_30,type,
    class_Rings_Ocomm__semiring__1: $i > $o ).

tff(decl_31,type,
    class_Groups_Oab__semigroup__add: $i > $o ).

tff(decl_32,type,
    class_Groups_Ocancel__semigroup__add: $i > $o ).

tff(decl_33,type,
    c_Polynomial_Odegree: ( $i * $i ) > $i ).

tff(decl_34,type,
    class_Groups_Ocancel__ab__semigroup__add: $i > $o ).

tff(decl_35,type,
    c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).

tff(decl_36,type,
    class_Groups_Ocomm__monoid__add: $i > $o ).

tff(decl_37,type,
    c_Polynomial_Omonom: ( $i * $i * $i ) > $i ).

tff(decl_38,type,
    tc_Complex_Ocomplex: $i ).

tff(decl_39,type,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).

tff(decl_40,type,
    tc_Nat_Onat: $i ).

tff(decl_41,type,
    c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).

tff(decl_42,type,
    c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).

tff(decl_43,type,
    class_Rings_Olinordered__idom: $i > $o ).

tff(decl_44,type,
    c_Polynomial_Opos__poly: ( $i * $i ) > $o ).

tff(decl_45,type,
    c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).

tff(decl_46,type,
    c_Polynomial_Ocoeff: ( $i * $i ) > $i ).

tff(decl_47,type,
    c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).

tff(decl_48,type,
    c_Groups_Osemigroup: ( $i * $i ) > $o ).

tff(decl_49,type,
    class_Groups_Ozero: $i > $o ).

tff(decl_50,type,
    class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).

tff(decl_51,type,
    class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).

tff(decl_52,type,
    class_Groups_Oordered__ab__semigroup__add: $i > $o ).

tff(decl_53,type,
    class_Orderings_Opreorder: $i > $o ).

tff(decl_54,type,
    c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).

tff(decl_55,type,
    class_Orderings_Oorder: $i > $o ).

tff(decl_56,type,
    class_Orderings_Oord: $i > $o ).

tff(decl_57,type,
    tc_fun: ( $i * $i ) > $i ).

tff(decl_58,type,
    class_Orderings_Olinorder: $i > $o ).

tff(decl_59,type,
    hBOOL: $i > $o ).

tff(decl_60,type,
    tc_RealDef_Oreal: $i ).

tff(decl_61,type,
    c_Groups_Ozero__class_Ozero: $i > $i ).

tff(decl_62,type,
    v_e: $i ).

tff(decl_63,type,
    c_Nat_Onat_Onat__case: ( $i * $i * $i ) > $i ).

tff(decl_64,type,
    c_Groups_Otimes__class_Otimes: $i > $i ).

tff(decl_65,type,
    c_Nat_OSuc: $i > $i ).

tff(decl_66,type,
    class_Groups_Oab__semigroup__mult: $i > $o ).

tff(decl_67,type,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).

tff(decl_68,type,
    class_Groups_Omonoid__add: $i > $o ).

tff(decl_69,type,
    class_Groups_Olinordered__ab__group__add: $i > $o ).

tff(decl_70,type,
    class_Groups_Oordered__comm__monoid__add: $i > $o ).

tff(decl_71,type,
    class_Rings_Olinordered__ring: $i > $o ).

tff(decl_72,type,
    class_Rings_Olinordered__ring__strict: $i > $o ).

tff(decl_73,type,
    class_Rings_Olinordered__semiring__strict: $i > $o ).

tff(decl_74,type,
    class_Rings_Olinordered__semiring: $i > $o ).

tff(decl_75,type,
    class_Rings_Omult__zero: $i > $o ).

tff(decl_76,type,
    class_Rings_Oring__no__zero__divisors: $i > $o ).

tff(decl_77,type,
    class_Rings_Ono__zero__divisors: $i > $o ).

tff(decl_78,type,
    class_Rings_Osemiring: $i > $o ).

tff(decl_79,type,
    class_Rings_Ocomm__semiring: $i > $o ).

tff(decl_80,type,
    class_Rings_Oordered__cancel__semiring: $i > $o ).

tff(decl_81,type,
    class_Rings_Oordered__ring: $i > $o ).

tff(decl_82,type,
    class_Rings_Oordered__semiring: $i > $o ).

tff(decl_83,type,
    class_Rings_Oordered__comm__semiring: $i > $o ).

tff(decl_84,type,
    class_Rings_Olinordered__comm__semiring__strict: $i > $o ).

tff(decl_85,type,
    class_Rings_Olinordered__semidom: $i > $o ).

tff(decl_86,type,
    c_Polynomial_Oorder: ( $i * $i * $i ) > $i ).

tff(decl_87,type,
    class_Fields_Ofield: $i > $o ).

tff(decl_88,type,
    c_Polynomial_Opdivmod__rel: ( $i * $i * $i * $i * $i ) > $o ).

tff(decl_89,type,
    class_RealVector_Oreal__normed__algebra: $i > $o ).

tff(decl_90,type,
    c_Polynomial_Opoly__rec: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_91,type,
    c_Polynomial_OAbs__poly: ( $i * $i ) > $i ).

tff(decl_92,type,
    c_fequal: ( $i * $i ) > $i ).

tff(decl_93,type,
    c_If: ( $i * $i * $i * $i ) > $i ).

tff(decl_94,type,
    class_Rings_Olinordered__semiring__1__strict: $i > $o ).

tff(decl_95,type,
    c_Groups_Oone__class_Oone: $i > $i ).

tff(decl_96,type,
    c_NthRoot_Oroot: ( $i * $i ) > $i ).

tff(decl_97,type,
    class_Groups_Omonoid__mult: $i > $o ).

tff(decl_98,type,
    class_Groups_Ocomm__monoid__mult: $i > $o ).

tff(decl_99,type,
    class_Rings_Ozero__neq__one: $i > $o ).

tff(decl_100,type,
    class_Groups_Oone: $i > $o ).

tff(decl_101,type,
    class_Rings_Olinordered__semiring__1: $i > $o ).

tff(decl_102,type,
    class_Rings_Ocomm__ring__1: $i > $o ).

tff(decl_103,type,
    c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).

tff(decl_104,type,
    c_Polynomial_Opoly__gcd: ( $i * $i * $i ) > $i ).

tff(decl_105,type,
    c_Power_Opower__class_Opower: $i > $i ).

tff(decl_106,type,
    class_Groups_Oordered__ab__group__add: $i > $o ).

tff(decl_107,type,
    class_Groups_Ogroup__add: $i > $o ).

tff(decl_108,type,
    class_Groups_Oab__group__add: $i > $o ).

tff(decl_109,type,
    class_Rings_Ocomm__ring: $i > $o ).

tff(decl_110,type,
    class_Rings_Oring: $i > $o ).

tff(decl_111,type,
    class_Rings_Oring__1__no__zero__divisors: $i > $o ).

tff(decl_112,type,
    tc_Int_Oint: $i ).

tff(decl_113,type,
    class_Power_Opower: $i > $o ).

tff(decl_114,type,
    class_Rings_Osemiring__0: $i > $o ).

tff(decl_115,type,
    class_Rings_Oring__1: $i > $o ).

tff(decl_116,type,
    c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).

tff(decl_117,type,
    c_Rings_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).

tff(decl_118,type,
    class_Rings_Odvd: $i > $o ).

tff(decl_119,type,
    class_Lattices_Oboolean__algebra: $i > $o ).

tff(decl_120,type,
    class_Lattices_Oab__semigroup__idem__mult: $i > $o ).

tff(decl_121,type,
    class_Groups_Ouminus: $i > $o ).

tff(decl_122,type,
    c_RComplete_Onatceiling: $i > $i ).

tff(decl_123,type,
    c_Rings_Oinverse__class_Oinverse: ( $i * $i ) > $i ).

tff(decl_124,type,
    class_Rings_Odivision__ring: $i > $o ).

tff(decl_125,type,
    class_Rings_Odivision__ring__inverse__zero: $i > $o ).

tff(decl_126,type,
    class_Fields_Olinordered__field__inverse__zero: $i > $o ).

tff(decl_127,type,
    class_Fields_Ofield__inverse__zero: $i > $o ).

tff(decl_128,type,
    class_Fields_Olinordered__field: $i > $o ).

tff(decl_129,type,
    c_RComplete_Onatfloor: $i > $i ).

tff(decl_130,type,
    c_RealDef_Oreal: ( $i * $i ) > $i ).

tff(decl_131,type,
    c_SEQ_Odecseq: ( $i * $i ) > $o ).

tff(decl_132,type,
    c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).

tff(decl_133,type,
    class_Divides_Osemiring__div: $i > $o ).

tff(decl_134,type,
    class_Divides_Oring__div: $i > $o ).

tff(decl_135,type,
    class_Groups_Ocancel__comm__monoid__add: $i > $o ).

tff(decl_136,type,
    tc_HOL_Obool: $i ).

tff(decl_137,type,
    v_p: $i ).

tff(decl_138,type,
    v_z: $i ).

tff(decl_139,type,
    v_thesis____: $o ).

tff(decl_140,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_141,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_142,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_143,type,
    esk4_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_144,type,
    esk5_2: ( $i * $i ) > $i ).

tff(decl_145,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_146,type,
    esk7_1: $i > $i ).

tff(decl_147,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_148,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_149,type,
    esk10_3: ( $i * $i * $i ) > $i ).

tff(decl_150,type,
    esk11_3: ( $i * $i * $i ) > $i ).

tff(decl_151,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_152,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_153,type,
    esk14_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_154,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_155,type,
    esk16_2: ( $i * $i ) > $i ).

tff(decl_156,type,
    esk17_2: ( $i * $i ) > $i ).

tff(decl_157,type,
    esk18_2: ( $i * $i ) > $i ).

tff(decl_158,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_159,type,
    esk20_2: ( $i * $i ) > $i ).

tff(decl_160,type,
    esk21_2: ( $i * $i ) > $i ).

tff(decl_161,type,
    esk22_1: $i > $i ).

tff(decl_162,type,
    esk23_1: $i > $i ).

tff(decl_163,type,
    esk24_1: $i > $i ).

fof(conj_0,hypothesis,
    ! [X19] :
      ( c_Polynomial_Odegree(tc_Complex_Ocomplex,X19) = c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)
     => ( ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X19),X3) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,X3))
       => v_thesis____ ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

fof(conj_1,conjecture,
    v_thesis____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).

fof(fact_poly__offset__poly,axiom,
    ! [X4,X8,X6,X7] :
      ( class_Rings_Ocomm__semiring__0(X7)
     => hAPP(c_Polynomial_Opoly(X7,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X7,X6,X8)),X4) = hAPP(c_Polynomial_Opoly(X7,X6),c_Groups_Oplus__class_Oplus(X7,X8,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__offset__poly) ).

fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
    class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).

fof(fact_degree__offset__poly,axiom,
    ! [X8,X6,X7] :
      ( class_Rings_Ocomm__semiring__0(X7)
     => c_Polynomial_Odegree(X7,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X7,X6,X8)) = c_Polynomial_Odegree(X7,X6) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_degree__offset__poly) ).

fof(c_0_5,hypothesis,
    ! [X2925] :
      ( c_Polynomial_Odegree(tc_Complex_Ocomplex,X2925) != c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)
      | hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X2925),esk24_1(X2925)) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,esk24_1(X2925)))
      | v_thesis____ ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_0])])]) ).

fof(c_0_6,negated_conjecture,
    ~ v_thesis____,
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_1])]) ).

cnf(c_0_7,hypothesis,
    ( v_thesis____
    | c_Polynomial_Odegree(tc_Complex_Ocomplex,X1) != c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p)
    | hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),esk24_1(X1)) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,esk24_1(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,negated_conjecture,
    ~ v_thesis____,
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_9,plain,
    ! [X97,X98,X99,X100] :
      ( ~ class_Rings_Ocomm__semiring__0(X100)
      | hAPP(c_Polynomial_Opoly(X100,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X100,X99,X98)),X97) = hAPP(c_Polynomial_Opoly(X100,X99),c_Groups_Oplus__class_Oplus(X100,X98,X97)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__offset__poly])]) ).

cnf(c_0_10,hypothesis,
    ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),esk24_1(X1)) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,esk24_1(X1)))
    | c_Polynomial_Odegree(tc_Complex_Ocomplex,X1) != c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) ),
    inference(sr,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,plain,
    ( hAPP(c_Polynomial_Opoly(X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3)),X4) = hAPP(c_Polynomial_Opoly(X1,X2),c_Groups_Oplus__class_Oplus(X1,X3,X4))
    | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_12,plain,
    class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).

cnf(c_0_13,hypothesis,
    ( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X1),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X2,esk24_1(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,X1,X2)))) != hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,esk24_1(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,X1,X2))))
    | c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,X1,X2)) != c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12])]) ).

fof(c_0_14,plain,
    ! [X140,X141,X142] :
      ( ~ class_Rings_Ocomm__semiring__0(X142)
      | c_Polynomial_Odegree(X142,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X142,X141,X140)) = c_Polynomial_Odegree(X142,X141) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_degree__offset__poly])]) ).

cnf(c_0_15,hypothesis,
    c_Polynomial_Odegree(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex,v_p,v_z)) != c_Polynomial_Odegree(tc_Complex_Ocomplex,v_p),
    inference(er,[status(thm)],[c_0_13]) ).

cnf(c_0_16,plain,
    ( c_Polynomial_Odegree(X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X1,X2,X3)) = c_Polynomial_Odegree(X1,X2)
    | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_17,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_12])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SWW213+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n016.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun Aug 27 22:42:29 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 10.11/10.18  % Version  : CSE_E---1.5
% 10.11/10.18  % Problem  : theBenchmark.p
% 10.11/10.18  % Proof found
% 10.11/10.18  % SZS status Theorem for theBenchmark.p
% 10.11/10.18  % SZS output start Proof
% See solution above
% 10.11/10.19  % Total time : 9.574000 s
% 10.11/10.19  % SZS output end Proof
% 10.11/10.19  % Total time : 9.615000 s
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