TSTP Solution File: SWW258+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWW258+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n019.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 : Tue Aug 22 11:06:56 EDT 2023

% Result   : Theorem 164.33s 136.14s
% Output   : CNFRefutation 164.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :  174
% Syntax   : Number of formulae    :  219 (  35 unt; 151 typ;   0 def)
%            Number of atoms       :  123 (  34 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  102 (  47   ~;  36   |;   0   &)
%                                         (   6 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  190 ( 123   >;  67   *;   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   :   64 (;  64   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_Rings_Odvd__class_Odvd > c_Orderings_Oord__class_Oless__eq > c_Orderings_Oord__class_Oless > c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant > c_SEQ_Odecseq > c_Polynomial_Opos__poly > hBOOL > class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct > class_Rings_Ozero__neq__one > class_Rings_Osemiring__0 > class_Rings_Osemiring > class_Rings_Oring__no__zero__divisors > class_Rings_Oring__1__no__zero__divisors > class_Rings_Oring__1 > class_Rings_Oring > class_Rings_Oordered__semiring > class_Rings_Oordered__ring > class_Rings_Oordered__comm__semiring > class_Rings_Oordered__cancel__semiring > class_Rings_Ono__zero__divisors > class_Rings_Omult__zero > class_Rings_Olinordered__semiring__strict > class_Rings_Olinordered__semiring__1__strict > class_Rings_Olinordered__semiring__1 > class_Rings_Olinordered__semiring > class_Rings_Olinordered__semidom > class_Rings_Olinordered__ring__strict > class_Rings_Olinordered__ring > class_Rings_Olinordered__idom > class_Rings_Olinordered__comm__semiring__strict > class_Rings_Oidom > class_Rings_Odvd > class_Rings_Odivision__ring__inverse__zero > class_Rings_Odivision__ring > class_Rings_Ocomm__semiring__1 > class_Rings_Ocomm__semiring__0 > class_Rings_Ocomm__semiring > class_Rings_Ocomm__ring__1 > class_Rings_Ocomm__ring > class_RealVector_Oreal__normed__vector > class_RealVector_Oreal__normed__div__algebra > class_RealVector_Oreal__normed__algebra__1 > class_RealVector_Oreal__normed__algebra > class_Power_Opower > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Oord > class_Orderings_Olinorder > class_Lattices_Oboolean__algebra > class_Lattices_Oab__semigroup__idem__mult > class_Int_Oring__char__0 > class_Groups_Ozero > class_Groups_Ouminus > class_Groups_Osgn__if > class_Groups_Oordered__comm__monoid__add > class_Groups_Oordered__cancel__ab__semigroup__add > class_Groups_Oordered__ab__semigroup__add__imp__le > class_Groups_Oordered__ab__semigroup__add > class_Groups_Oordered__ab__group__add > class_Groups_Oone > class_Groups_Omonoid__mult > class_Groups_Omonoid__add > class_Groups_Ominus > class_Groups_Olinordered__ab__group__add > class_Groups_Ogroup__add > class_Groups_Ocomm__monoid__mult > class_Groups_Ocomm__monoid__add > class_Groups_Ocancel__semigroup__add > class_Groups_Ocancel__comm__monoid__add > class_Groups_Ocancel__ab__semigroup__add > class_Groups_Oab__semigroup__mult > class_Groups_Oab__semigroup__add > class_Groups_Oab__group__add > class_Fields_Olinordered__field__inverse__zero > class_Fields_Olinordered__field > class_Fields_Ofield__inverse__zero > class_Fields_Ofield > c_Power_Opower_Opower > c_Polynomial_Osynthetic__div > c_Polynomial_Osmult > c_Polynomial_Opcompose > c_Polynomial_OpCons > c_Polynomial_Oorder > c_Polynomial_Omonom > c_Groups_Oplus__class_Oplus > c_Groups_Ominus__class_Ominus > tc_fun > hAPP > c_Rings_Oinverse__class_Oinverse > c_RealVector_Onorm__class_Onorm > c_Polynomial_Opoly > c_Nat__Transfer_Otsub > c_Groups_Ouminus__class_Ouminus > c_Groups_Osgn__class_Osgn > c_Fundamental__Theorem__Algebra__Mirabelle_Opsize > #nlpp > tc_Polynomial_Opoly > c_Power_Opower__class_Opower > c_Nat_OSuc > c_Groups_Ozero__class_Ozero > c_Groups_Otimes__class_Otimes > c_Groups_Oone__class_Oone > v_w____ > v_s____ > v_q____ > v_pa____ > v_p > v_m____ > v_k____ > v_c____ > v_a____ > tc_RealDef_Oreal > tc_Nat_Onat > tc_Int_Oint > tc_HOL_Obool > tc_Complex_Ocomplex > c_Complex_Oii > #skF_32 > #skF_35 > #skF_31 > #skF_20 > #skF_18 > #skF_17 > #skF_11 > #skF_6 > #skF_30 > #skF_15 > #skF_19 > #skF_34 > #skF_16 > #skF_14 > #skF_13 > #skF_5 > #skF_3 > #skF_8 > #skF_21 > #skF_9 > #skF_33 > #skF_26 > #skF_4 > #skF_25 > #skF_2 > #skF_24 > #skF_12 > #skF_7 > #skF_29 > #skF_27 > #skF_1 > #skF_22 > #skF_28 > #skF_23 > #skF_10

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(class_Groups_Olinordered__ab__group__add,type,
    class_Groups_Olinordered__ab__group__add: $i > $o ).

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

tff('#skF_32',type,
    '#skF_32': ( $i * $i * $i ) > $i ).

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

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

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

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

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

tff('#skF_35',type,
    '#skF_35': ( $i * $i ) > $i ).

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

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

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

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

tff('#skF_31',type,
    '#skF_31': ( $i * $i * $i ) > $i ).

tff('#skF_20',type,
    '#skF_20': $i ).

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

tff('#skF_18',type,
    '#skF_18': $i ).

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

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

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

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

tff('#skF_17',type,
    '#skF_17': $i ).

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

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

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

tff('#skF_11',type,
    '#skF_11': $i ).

tff('#skF_6',type,
    '#skF_6': ( $i * $i * $i ) > $i ).

tff('#skF_30',type,
    '#skF_30': ( $i * $i ) > $i ).

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

tff('#skF_15',type,
    '#skF_15': $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff('#skF_19',type,
    '#skF_19': $i ).

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

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

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

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

tff('#skF_34',type,
    '#skF_34': ( $i * $i ) > $i ).

tff('#skF_16',type,
    '#skF_16': $i ).

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

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

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

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

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

tff('#skF_14',type,
    '#skF_14': $i ).

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

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

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

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

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

tff('#skF_13',type,
    '#skF_13': $i ).

tff('#skF_5',type,
    '#skF_5': ( $i * $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

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

tff('#skF_3',type,
    '#skF_3': $i ).

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

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

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

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

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

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

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

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

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

tff('#skF_8',type,
    '#skF_8': ( $i * $i ) > $i ).

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

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

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

tff('#skF_21',type,
    '#skF_21': $i ).

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

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

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

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

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

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

tff('#skF_9',type,
    '#skF_9': ( $i * $i * $i ) > $i ).

tff('#skF_33',type,
    '#skF_33': $i > $i ).

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

tff('#skF_26',type,
    '#skF_26': $i > $i ).

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

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

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

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

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

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

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

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

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

tff(hAPP,type,
    hAPP: ( $i * $i ) > $i ).

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

tff('#skF_4',type,
    '#skF_4': $i ).

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

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

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

tff('#skF_25',type,
    '#skF_25': ( $i * $i ) > $i ).

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

tff('#skF_2',type,
    '#skF_2': ( $i * $i ) > $i ).

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

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

tff('#skF_24',type,
    '#skF_24': $i ).

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

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

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

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

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

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

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

tff('#skF_12',type,
    '#skF_12': $i > $i ).

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

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

tff('#skF_7',type,
    '#skF_7': ( $i * $i ) > $i ).

tff('#skF_29',type,
    '#skF_29': ( $i * $i ) > $i ).

tff('#skF_27',type,
    '#skF_27': ( $i * $i ) > $i ).

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

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

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

tff('#skF_1',type,
    '#skF_1': ( $i * $i ) > $i ).

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

tff('#skF_22',type,
    '#skF_22': ( $i * $i * $i * $i ) > $i ).

tff('#skF_28',type,
    '#skF_28': ( $i * $i * $i ) > $i ).

tff('#skF_23',type,
    '#skF_23': ( $i * $i * $i * $i ) > $i ).

tff('#skF_10',type,
    '#skF_10': ( $i * $i * $i ) > $i ).

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

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

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

tff(f_35,axiom,
    v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_w0) ).

tff(f_5840,axiom,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

tff(f_84,axiom,
    ! [V_x_2,T_a] :
      ( class_RealVector_Oreal__normed__vector(T_a)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))
      <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).

tff(f_5792,axiom,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).

tff(f_1062,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
       => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).

tff(f_5788,axiom,
    class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).

tff(f_1596,axiom,
    ! [V_y_2,V_x_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
    <=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
        | ( V_x_2 = V_y_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__real__def) ).

tff(f_5815,axiom,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).

tff(f_1854,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => ( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = V_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).

tff(f_5799,axiom,
    class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).

tff(f_2782,axiom,
    ! [V_y_2,V_x_2] :
      ( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
    <=> ( V_y_2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__eq__0__iff) ).

tff(f_1465,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).

tff(f_1834,axiom,
    ! [V_b_2,V_aa_2,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) )
      <=> ( V_aa_2 = V_b_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).

tff(f_2079,axiom,
    ! [V_aa_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))
      <=> c_Orderings_Oord__class_Oless__eq(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).

tff(f_5809,axiom,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).

tff(f_33,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) ).

tff(f_4091,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
       => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
         => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).

tff(f_1737,axiom,
    ! [V_y,V_x] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
       => 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),V_x),V_y)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__order) ).

tff(f_5770,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) ).

tff(f_1185,axiom,
    ! [V_aa_2,T_a] :
      ( class_Fields_Olinordered__field__inverse__zero(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2))
      <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__positive__iff__positive) ).

tff(f_1451,axiom,
    ! [V_w,V_z] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).

tff(f_5388,axiom,
    ! [V_n] : ( c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).

tff(f_6104,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____))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

tff(c_6,plain,
    c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) != v_w____,
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_3194,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(cnfTransformation,[status(thm)],[f_5840]) ).

tff(c_22,plain,
    ! [T_a_23,V_x_2_22] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a_23,V_x_2_22))
      | ( c_Groups_Ozero__class_Ozero(T_a_23) = V_x_2_22 )
      | ~ class_RealVector_Oreal__normed__vector(T_a_23) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_3098,plain,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_5792]) ).

tff(c_389,plain,
    ! [T_a_428,V_a_427,V_n_426] :
      ( c_Orderings_Oord__class_Oless(T_a_428,c_Groups_Ozero__class_Ozero(T_a_428),hAPP(hAPP(c_Power_Opower__class_Opower(T_a_428),V_a_427),V_n_426))
      | ~ c_Orderings_Oord__class_Oless(T_a_428,c_Groups_Ozero__class_Ozero(T_a_428),V_a_427)
      | ~ class_Rings_Olinordered__semidom(T_a_428) ),
    inference(cnfTransformation,[status(thm)],[f_1062]) ).

tff(c_3090,plain,
    class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_5788]) ).

tff(c_626,plain,
    ! [V_y_2_689] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2_689,V_y_2_689),
    inference(cnfTransformation,[status(thm)],[f_1596]) ).

tff(c_3144,plain,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_5815]) ).

tff(c_761,plain,
    ! [T_a_801,V_a_800] :
      ( ( c_Groups_Ouminus__class_Ouminus(T_a_801,c_Groups_Ouminus__class_Ouminus(T_a_801,V_a_800)) = V_a_800 )
      | ~ class_Groups_Ogroup__add(T_a_801) ),
    inference(cnfTransformation,[status(thm)],[f_1854]) ).

tff(c_3112,plain,
    class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_5799]) ).

tff(c_5681,plain,
    ! [V_x_2_3009] : ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2_3009,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2_3009)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(cnfTransformation,[status(thm)],[f_2782]) ).

tff(c_564,plain,
    ! [T_a_614,V_a_613] :
      ( ( c_Groups_Oplus__class_Oplus(T_a_614,c_Groups_Ozero__class_Ozero(T_a_614),V_a_613) = V_a_613 )
      | ~ class_Groups_Ocomm__monoid__add(T_a_614) ),
    inference(cnfTransformation,[status(thm)],[f_1465]) ).

tff(c_5687,plain,
    ( ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
    | ~ class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_5681,c_564]) ).

tff(c_5720,plain,
    c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(demodulation,[status(thm),theory(equality)],[c_3112,c_5687]) ).

tff(c_10958,plain,
    ! [V_b_2_3158,V_aa_2_3159,T_a_3160] :
      ( ( V_b_2_3158 = V_aa_2_3159 )
      | ( c_Groups_Ouminus__class_Ouminus(T_a_3160,V_b_2_3158) != c_Groups_Ouminus__class_Ouminus(T_a_3160,V_aa_2_3159) )
      | ~ class_Groups_Ogroup__add(T_a_3160) ),
    inference(cnfTransformation,[status(thm)],[f_1834]) ).

tff(c_10962,plain,
    ! [V_b_2_3158] :
      ( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = V_b_2_3158 )
      | ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_b_2_3158) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ~ class_Groups_Ogroup__add(tc_RealDef_Oreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_5720,c_10958]) ).

tff(c_11668,plain,
    ! [V_b_2_3176] :
      ( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = V_b_2_3176 )
      | ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_b_2_3176) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3144,c_10962]) ).

tff(c_11675,plain,
    ! [V_a_800] :
      ( ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_800) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != V_a_800 )
      | ~ class_Groups_Ogroup__add(tc_RealDef_Oreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_761,c_11668]) ).

tff(c_11691,plain,
    ! [V_a_800] :
      ( ( c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_800) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != V_a_800 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3144,c_11675]) ).

tff(c_126602,plain,
    ! [T_a_139278,V_aa_2_139279] :
      ( c_Orderings_Oord__class_Oless__eq(T_a_139278,V_aa_2_139279,c_Groups_Ozero__class_Ozero(T_a_139278))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a_139278,c_Groups_Ozero__class_Ozero(T_a_139278),c_Groups_Ouminus__class_Ouminus(T_a_139278,V_aa_2_139279))
      | ~ class_Groups_Oordered__ab__group__add(T_a_139278) ),
    inference(cnfTransformation,[status(thm)],[f_2079]) ).

tff(c_126720,plain,
    ! [V_a_800] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_a_800,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | ~ class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal)
      | ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != V_a_800 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_11691,c_126602]) ).

tff(c_126809,plain,
    ! [V_a_800] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_a_800,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != V_a_800 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3090,c_626,c_126720]) ).

tff(c_3132,plain,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_5809]) ).

tff(c_4,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_104403,plain,
    ! [T_a_123939,V_x_123940,V_z_123941,V_y_123942] :
      ( c_Orderings_Oord__class_Oless(T_a_123939,V_x_123940,V_z_123941)
      | ~ c_Orderings_Oord__class_Oless(T_a_123939,V_y_123942,V_z_123941)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a_123939,V_x_123940,V_y_123942)
      | ~ class_Orderings_Opreorder(T_a_123939) ),
    inference(cnfTransformation,[status(thm)],[f_4091]) ).

tff(c_104583,plain,
    ! [V_x_123940] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_123940,v_m____)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_123940,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | ~ class_Orderings_Opreorder(tc_RealDef_Oreal) ),
    inference(resolution,[status(thm)],[c_4,c_104403]) ).

tff(c_288583,plain,
    ! [V_x_230374] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_230374,v_m____)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_230374,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3132,c_104583]) ).

tff(c_288754,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
    inference(resolution,[status(thm)],[c_126809,c_288583]) ).

tff(c_364760,plain,
    ! [V_x_267291,V_y_267292] :
      ( 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),V_x_267291),V_y_267292))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_267292)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_267291) ),
    inference(cnfTransformation,[status(thm)],[f_1737]) ).

tff(c_3054,plain,
    class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_5770]) ).

tff(c_91272,plain,
    ! [T_a_112911,V_aa_2_112912] :
      ( c_Orderings_Oord__class_Oless(T_a_112911,c_Groups_Ozero__class_Ozero(T_a_112911),c_Rings_Oinverse__class_Oinverse(T_a_112911,V_aa_2_112912))
      | ~ c_Orderings_Oord__class_Oless(T_a_112911,c_Groups_Ozero__class_Ozero(T_a_112911),V_aa_2_112912)
      | ~ class_Fields_Olinordered__field__inverse__zero(T_a_112911) ),
    inference(cnfTransformation,[status(thm)],[f_1185]) ).

tff(c_554,plain,
    ! [V_z_603,V_w_602] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_603),V_w_602) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w_602),V_z_603) ),
    inference(cnfTransformation,[status(thm)],[f_1451]) ).

tff(c_2665,plain,
    ! [V_n_2621] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2621,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Nat_OSuc(V_n_2621) ),
    inference(cnfTransformation,[status(thm)],[f_5388]) ).

tff(c_3376,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),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(cnfTransformation,[status(thm)],[f_6104]) ).

tff(c_3392,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),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____))),v_m____))),
    inference(demodulation,[status(thm),theory(equality)],[c_2665,c_3376]) ).

tff(c_3506,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),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____))))),
    inference(demodulation,[status(thm),theory(equality)],[c_554,c_3392]) ).

tff(c_91338,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),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____))))
    | ~ class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal) ),
    inference(resolution,[status(thm)],[c_91272,c_3506]) ).

tff(c_91596,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),v_m____),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Nat_OSuc(v_k____)))),
    inference(demodulation,[status(thm),theory(equality)],[c_3054,c_91338]) ).

tff(c_364790,plain,
    ( ~ 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_Nat_OSuc(v_k____)))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____) ),
    inference(resolution,[status(thm)],[c_364760,c_91596]) ).

tff(c_365063,plain,
    ~ 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_Nat_OSuc(v_k____))),
    inference(demodulation,[status(thm),theory(equality)],[c_288754,c_364790]) ).

tff(c_365188,plain,
    ( ~ 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____))
    | ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ),
    inference(resolution,[status(thm)],[c_389,c_365063]) ).

tff(c_365228,plain,
    ~ 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(demodulation,[status(thm),theory(equality)],[c_3098,c_365188]) ).

tff(c_365278,plain,
    ( ( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v_w____ )
    | ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
    inference(resolution,[status(thm)],[c_22,c_365228]) ).

tff(c_365301,plain,
    c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = v_w____,
    inference(demodulation,[status(thm),theory(equality)],[c_3194,c_365278]) ).

tff(c_365303,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_6,c_365301]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SWW258+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.15  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.37  % Computer : n019.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Thu Aug  3 19:09:16 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 164.33/136.14  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 164.33/136.16  
% 164.33/136.16  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 164.48/136.20  
% 164.48/136.20  Inference rules
% 164.48/136.20  ----------------------
% 164.48/136.20  #Ref     : 132
% 164.48/136.20  #Sup     : 72715
% 164.48/136.20  #Fact    : 16
% 164.48/136.20  #Define  : 0
% 164.48/136.20  #Split   : 32
% 164.48/136.20  #Chain   : 0
% 164.48/136.20  #Close   : 0
% 164.48/136.20  
% 164.48/136.20  Ordering : KBO
% 164.62/136.20  
% 164.62/136.20  Simplification rules
% 164.62/136.20  ----------------------
% 164.62/136.20  #Subsume      : 25302
% 164.62/136.20  #Demod        : 44081
% 164.62/136.20  #Tautology    : 13300
% 164.62/136.20  #SimpNegUnit  : 3127
% 164.62/136.20  #BackRed      : 51
% 164.62/136.20  
% 164.62/136.20  #Partial instantiations: 134514
% 164.62/136.20  #Strategies tried      : 1
% 164.62/136.20  
% 164.62/136.20  Timing (in seconds)
% 164.62/136.20  ----------------------
% 164.62/136.20  Preprocessing        : 2.21
% 164.62/136.20  Parsing              : 1.22
% 164.62/136.20  CNF conversion       : 0.18
% 164.62/136.20  Main loop            : 132.88
% 164.62/136.20  Inferencing          : 13.03
% 164.62/136.20  Reduction            : 76.07
% 164.62/136.20  Demodulation         : 59.81
% 164.62/136.20  BG Simplification    : 0.59
% 164.62/136.20  Subsumption          : 33.67
% 164.62/136.20  Abstraction          : 0.77
% 164.62/136.20  MUC search           : 0.00
% 164.62/136.20  Cooper               : 0.00
% 164.62/136.20  Total                : 135.16
% 164.62/136.20  Index Insertion      : 0.00
% 164.62/136.20  Index Deletion       : 0.00
% 164.62/136.20  Index Matching       : 0.00
% 164.62/136.21  BG Taut test         : 0.00
%------------------------------------------------------------------------------