TSTP Solution File: SWW258+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWW258+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 : n008.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 00:16:45 EDT 2023

% Result   : Theorem 10.83s 10.99s
% Output   : CNFRefutation 10.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :  161
% Syntax   : Number of formulae    :  181 (  16 unt; 151 typ;   0 def)
%            Number of atoms       :   63 (   7 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   61 (  28   ~;  23   |;   2   &)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  186 ( 123   >;  63   *;   0   +;   0  <<)
%            Number of predicates  :   79 (  77 usr;   1 prp; 0-3 aty)
%            Number of functors    :   74 (  74 usr;  28 con; 0-4 aty)
%            Number of variables   :   30 (   1 sgn;  18   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    hAPP: ( $i * $i ) > $i ).

tff(decl_23,type,
    tc_RealDef_Oreal: $i ).

tff(decl_24,type,
    c_Groups_Ozero__class_Ozero: $i > $i ).

tff(decl_25,type,
    v_m____: $i ).

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

tff(decl_27,type,
    v_w____: $i ).

tff(decl_28,type,
    tc_Complex_Ocomplex: $i ).

tff(decl_29,type,
    c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).

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

tff(decl_31,type,
    v_k____: $i ).

tff(decl_32,type,
    tc_Nat_Onat: $i ).

tff(decl_33,type,
    class_Rings_Olinordered__semidom: $i > $o ).

tff(decl_34,type,
    c_Groups_Oone__class_Oone: $i > $i ).

tff(decl_35,type,
    c_Groups_Otimes__class_Otimes: $i > $i ).

tff(decl_36,type,
    c_Power_Opower__class_Opower: $i > $i ).

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

tff(decl_38,type,
    class_RealVector_Oreal__normed__div__algebra: $i > $o ).

tff(decl_39,type,
    class_RealVector_Oreal__normed__algebra: $i > $o ).

tff(decl_40,type,
    class_RealVector_Oreal__normed__vector: $i > $o ).

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

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

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

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

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

tff(decl_46,type,
    v_a____: $i ).

tff(decl_47,type,
    class_Groups_Omonoid__mult: $i > $o ).

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

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

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

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

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

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

tff(decl_54,type,
    class_Power_Opower: $i > $o ).

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

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

tff(decl_57,type,
    class_Rings_Olinordered__idom: $i > $o ).

tff(decl_58,type,
    class_RealVector_Oreal__normed__algebra__1: $i > $o ).

tff(decl_59,type,
    class_Rings_Olinordered__semiring__1: $i > $o ).

tff(decl_60,type,
    class_Rings_Odivision__ring__inverse__zero: $i > $o ).

tff(decl_61,type,
    class_Rings_Olinordered__semiring__1__strict: $i > $o ).

tff(decl_62,type,
    class_Rings_Ono__zero__divisors: $i > $o ).

tff(decl_63,type,
    class_Rings_Oring__no__zero__divisors: $i > $o ).

tff(decl_64,type,
    class_Rings_Omult__zero: $i > $o ).

tff(decl_65,type,
    class_Rings_Ozero__neq__one: $i > $o ).

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

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

tff(decl_68,type,
    class_Rings_Oring__1__no__zero__divisors: $i > $o ).

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

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

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

tff(decl_72,type,
    class_Rings_Osemiring__0: $i > $o ).

tff(decl_73,type,
    v_s____: $i ).

tff(decl_74,type,
    c_Polynomial_Opoly: ( $i * $i ) > $i ).

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

tff(decl_76,type,
    v_p: $i ).

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

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

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

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

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

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

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

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

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

tff(decl_86,type,
    class_Groups_Olinordered__ab__group__add: $i > $o ).

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

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

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

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

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

tff(decl_92,type,
    v_pa____: $i ).

tff(decl_93,type,
    class_Groups_Ogroup__add: $i > $o ).

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

tff(decl_95,type,
    class_Groups_Oordered__ab__group__add: $i > $o ).

tff(decl_96,type,
    class_Rings_Oidom: $i > $o ).

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

tff(decl_98,type,
    class_Rings_Oring__1: $i > $o ).

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

tff(decl_100,type,
    class_Rings_Ocomm__semiring__1: $i > $o ).

tff(decl_101,type,
    v_c____: $i ).

tff(decl_102,type,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: ( $i * $i ) > $i ).

tff(decl_103,type,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).

tff(decl_104,type,
    class_Rings_Ocomm__ring__1: $i > $o ).

tff(decl_105,type,
    v_q____: $i ).

tff(decl_106,type,
    c_Polynomial_Osmult: ( $i * $i * $i ) > $i ).

tff(decl_107,type,
    tc_Polynomial_Opoly: $i > $i ).

tff(decl_108,type,
    tc_Int_Oint: $i ).

tff(decl_109,type,
    c_Polynomial_OpCons: ( $i * $i * $i ) > $i ).

tff(decl_110,type,
    class_Rings_Ocomm__semiring__0: $i > $o ).

tff(decl_111,type,
    class_Int_Oring__char__0: $i > $o ).

tff(decl_112,type,
    class_Rings_Ocomm__ring: $i > $o ).

tff(decl_113,type,
    c_Polynomial_Omonom: ( $i * $i * $i ) > $i ).

tff(decl_114,type,
    c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).

tff(decl_115,type,
    c_Polynomial_Opcompose: ( $i * $i * $i ) > $i ).

tff(decl_116,type,
    c_Complex_Oii: $i ).

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

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

tff(decl_119,type,
    c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).

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

tff(decl_121,type,
    tc_fun: ( $i * $i ) > $i ).

tff(decl_122,type,
    class_Orderings_Olinorder: $i > $o ).

tff(decl_123,type,
    class_Orderings_Oorder: $i > $o ).

tff(decl_124,type,
    c_Nat__Transfer_Otsub: ( $i * $i ) > $i ).

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

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

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

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

tff(decl_129,type,
    class_Groups_Ominus: $i > $o ).

tff(decl_130,type,
    class_Groups_Ouminus: $i > $o ).

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

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

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

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

tff(decl_135,type,
    c_Nat_OSuc: $i > $i ).

tff(decl_136,type,
    class_Groups_Ocancel__comm__monoid__add: $i > $o ).

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

tff(decl_138,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_139,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_140,type,
    esk3_0: $i ).

tff(decl_141,type,
    esk4_0: $i ).

tff(decl_142,type,
    esk5_1: $i > $i ).

tff(decl_143,type,
    esk6_1: $i > $i ).

tff(decl_144,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_145,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_146,type,
    esk9_3: ( $i * $i * $i ) > $i ).

tff(decl_147,type,
    esk10_3: ( $i * $i * $i ) > $i ).

tff(decl_148,type,
    esk11_0: $i ).

tff(decl_149,type,
    esk12_1: $i > $i ).

tff(decl_150,type,
    esk13_0: $i ).

tff(decl_151,type,
    esk14_0: $i ).

tff(decl_152,type,
    esk15_0: $i ).

tff(decl_153,type,
    esk16_0: $i ).

tff(decl_154,type,
    esk17_0: $i ).

tff(decl_155,type,
    esk18_0: $i ).

tff(decl_156,type,
    esk19_0: $i ).

tff(decl_157,type,
    esk20_0: $i ).

tff(decl_158,type,
    esk21_0: $i ).

tff(decl_159,type,
    esk22_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_160,type,
    esk23_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_161,type,
    esk24_0: $i ).

tff(decl_162,type,
    esk25_2: ( $i * $i ) > $i ).

tff(decl_163,type,
    esk26_1: $i > $i ).

tff(decl_164,type,
    esk27_2: ( $i * $i ) > $i ).

tff(decl_165,type,
    esk28_3: ( $i * $i * $i ) > $i ).

tff(decl_166,type,
    esk29_2: ( $i * $i ) > $i ).

tff(decl_167,type,
    esk30_2: ( $i * $i ) > $i ).

tff(decl_168,type,
    esk31_3: ( $i * $i * $i ) > $i ).

tff(decl_169,type,
    esk32_3: ( $i * $i * $i ) > $i ).

tff(decl_170,type,
    esk33_1: $i > $i ).

tff(decl_171,type,
    esk34_2: ( $i * $i ) > $i ).

tff(decl_172,type,
    esk35_2: ( $i * $i ) > $i ).

fof(fact_inverse__positive__iff__positive,axiom,
    ! [X25,X6] :
      ( class_Fields_Olinordered__field__inverse__zero(X6)
     => ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),c_Rings_Oinverse__class_Oinverse(X6,X25))
      <=> c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X25) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__positive__iff__positive) ).

fof(fact_real__mult__order,axiom,
    ! [X8,X10] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X10)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X8)
       => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X10),X8)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__order) ).

fof(conj_0,conjecture,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
    class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).

fof(fact_m_I1_J,axiom,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_m_I1_J) ).

fof(fact_zero__less__power,axiom,
    ! [X4,X5,X6] :
      ( class_Rings_Olinordered__semidom(X6)
     => ( c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),X5)
       => c_Orderings_Oord__class_Oless(X6,c_Groups_Ozero__class_Ozero(X6),hAPP(hAPP(c_Power_Opower__class_Opower(X6),X5),X4)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).

fof(fact_zero__less__norm__iff,axiom,
    ! [X13,X6] :
      ( class_RealVector_Oreal__normed__vector(X6)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X6,X13))
      <=> X13 != c_Groups_Ozero__class_Ozero(X6) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).

fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).

fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

fof(fact_w0,axiom,
    v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_w0) ).

fof(c_0_10,plain,
    ! [X560,X561] :
      ( ( ~ c_Orderings_Oord__class_Oless(X561,c_Groups_Ozero__class_Ozero(X561),c_Rings_Oinverse__class_Oinverse(X561,X560))
        | c_Orderings_Oord__class_Oless(X561,c_Groups_Ozero__class_Ozero(X561),X560)
        | ~ class_Fields_Olinordered__field__inverse__zero(X561) )
      & ( ~ c_Orderings_Oord__class_Oless(X561,c_Groups_Ozero__class_Ozero(X561),X560)
        | c_Orderings_Oord__class_Oless(X561,c_Groups_Ozero__class_Ozero(X561),c_Rings_Oinverse__class_Oinverse(X561,X560))
        | ~ class_Fields_Olinordered__field__inverse__zero(X561) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__positive__iff__positive])])]) ).

fof(c_0_11,plain,
    ! [X836,X837] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X837)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X836)
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X837),X836)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__order])]) ).

fof(c_0_12,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

cnf(c_0_13,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_15,plain,
    class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero]) ).

cnf(c_0_16,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_17,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2)))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).

cnf(c_0_18,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
    inference(split_conjunct,[status(thm)],[fact_m_I1_J]) ).

fof(c_0_19,plain,
    ! [X515,X516,X517] :
      ( ~ class_Rings_Olinordered__semidom(X517)
      | ~ c_Orderings_Oord__class_Oless(X517,c_Groups_Ozero__class_Ozero(X517),X516)
      | c_Orderings_Oord__class_Oless(X517,c_Groups_Ozero__class_Ozero(X517),hAPP(hAPP(c_Power_Opower__class_Opower(X517),X516),X515)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power])]) ).

fof(c_0_20,plain,
    ! [X111,X112] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X112,X111))
        | X111 != c_Groups_Ozero__class_Ozero(X112)
        | ~ class_RealVector_Oreal__normed__vector(X112) )
      & ( X111 = c_Groups_Ozero__class_Ozero(X112)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X112,X111))
        | ~ class_RealVector_Oreal__normed__vector(X112) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__norm__iff])])]) ).

cnf(c_0_21,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).

cnf(c_0_22,plain,
    ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_23,plain,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).

cnf(c_0_24,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1))
    | ~ class_RealVector_Oreal__normed__vector(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_25,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).

cnf(c_0_26,negated_conjecture,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).

cnf(c_0_27,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_28,plain,
    v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(split_conjunct,[status(thm)],[fact_w0]) ).

cnf(c_0_29,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : SWW258+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.10  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.30  % Computer : n008.cluster.edu
% 0.12/0.30  % Model    : x86_64 x86_64
% 0.12/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30  % Memory   : 8042.1875MB
% 0.12/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30  % CPULimit   : 300
% 0.12/0.30  % WCLimit    : 300
% 0.12/0.30  % DateTime   : Sun Aug 27 17:53:02 EDT 2023
% 0.12/0.30  % CPUTime  : 
% 0.15/0.56  start to proof: theBenchmark
% 10.83/10.99  % Version  : CSE_E---1.5
% 10.83/10.99  % Problem  : theBenchmark.p
% 10.83/10.99  % Proof found
% 10.83/10.99  % SZS status Theorem for theBenchmark.p
% 10.83/10.99  % SZS output start Proof
% See solution above
% 10.96/11.01  % Total time : 10.394000 s
% 10.96/11.01  % SZS output end Proof
% 10.96/11.01  % Total time : 10.431000 s
%------------------------------------------------------------------------------