TSTP Solution File: SWW259+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWW259+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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n004.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 223.27s 185.33s
% Output   : CNFRefutation 223.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :  160
% Syntax   : Number of formulae    :  195 (  25 unt; 148 typ;   0 def)
%            Number of atoms       :  107 (  12 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  111 (  51   ~;  46   |;   2   &)
%                                         (   1 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  184 ( 119   >;  65   *;   0   +;   0  <<)
%            Number of predicates  :   75 (  73 usr;   2 prp; 0-3 aty)
%            Number of functors    :   75 (  75 usr;  28 con; 0-4 aty)
%            Number of variables   :   42 (;  41   !;   1   ?;   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_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_Int_Oring__char__0 > class_Groups_Ozero > 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_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 > class_Divides_Osemiring__div > 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 > c_Divides_Odiv__class_Odiv > 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_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 > c_Complex_Oexpi > v_w____ > v_thesis____ > 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_17 > #skF_2 > #skF_18 > #skF_35 > #skF_6 > #skF_15 > #skF_25 > #skF_19 > #skF_29 > #skF_34 > #skF_26 > #skF_12 > #skF_30 > #skF_14 > #skF_33 > #skF_13 > #skF_5 > #skF_10 > #skF_3 > #skF_8 > #skF_21 > #skF_32 > #skF_31 > #skF_23 > #skF_28 > #skF_11 > #skF_22 > #skF_24 > #skF_27 > #skF_7 > #skF_1 > #skF_9 > #skF_4 > #skF_20 > #skF_16

%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(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(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_17',type,
    '#skF_17': ( $i * $i * $i ) > $i ).

tff('#skF_2',type,
    '#skF_2': $i > $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(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('#skF_35',type,
    '#skF_35': $i > $i ).

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

tff('#skF_6',type,
    '#skF_6': ( $i * $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_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('#skF_25',type,
    '#skF_25': $i ).

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(v_thesis____,type,
    v_thesis____: $o ).

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

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

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

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

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

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

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

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

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

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

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('#skF_32',type,
    '#skF_32': $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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('#skF_27',type,
    '#skF_27': $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(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(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_9',type,
    '#skF_9': ( $i * $i ) > $i ).

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

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

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

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

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

tff(f_5712,axiom,
    class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).

tff(f_1466,axiom,
    ! [V_aa_2,T_a] :
      ( class_Groups_Olinordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)
      <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).

tff(f_5742,axiom,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).

tff(f_5734,axiom,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).

tff(f_175,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( ( V_x != V_y )
       => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
         => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).

tff(f_179,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/sandbox/benchmark/theBenchmark.p',fact_real__mult__commute) ).

tff(f_3130,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/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).

tff(f_6032,negated_conjecture,
    ~ v_thesis____,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).

tff(f_6030,hypothesis,
    ! [B_t] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_t)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
       => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t,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____)))
         => v_thesis____ ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(f_4740,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( c_Orderings_Oord__class_Oless(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/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).

tff(f_43,axiom,
    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/sandbox/benchmark/theBenchmark.p',fact_inv0) ).

tff(f_41,axiom,
    ! [V_d2] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2)
     => ? [B_e] :
          ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_e)
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_e,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_e,V_d2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bd2_O_A0_A_060_Ad2_A_061_061_062_AEX_Ae_0620_O_Ae_A_060_A1_A_G_Ae_A_060_Ad2_096) ).

tff(c_3031,plain,
    class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_5712]) ).

tff(c_682,plain,
    ! [T_a_716,V_aa_2_715] :
      ( c_Orderings_Oord__class_Oless(T_a_716,c_Groups_Ouminus__class_Ouminus(T_a_716,V_aa_2_715),V_aa_2_715)
      | ~ c_Orderings_Oord__class_Oless(T_a_716,c_Groups_Ozero__class_Ozero(T_a_716),V_aa_2_715)
      | ~ class_Groups_Olinordered__ab__group__add(T_a_716) ),
    inference(cnfTransformation,[status(thm)],[f_1466]) ).

tff(c_3091,plain,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_5742]) ).

tff(c_3075,plain,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_5734]) ).

tff(c_51042,plain,
    ! [T_a_3831,V_y_3832,V_x_3833] :
      ( c_Orderings_Oord__class_Oless(T_a_3831,V_y_3832,V_x_3833)
      | c_Orderings_Oord__class_Oless(T_a_3831,V_x_3833,V_y_3832)
      | ( V_y_3832 = V_x_3833 )
      | ~ class_Rings_Olinordered__idom(T_a_3831) ),
    inference(cnfTransformation,[status(thm)],[f_175]) ).

tff(c_68,plain,
    ! [V_z_58,V_w_57] : ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_58),V_w_57) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w_57),V_z_58) ),
    inference(cnfTransformation,[status(thm)],[f_179]) ).

tff(c_1727,plain,
    ! [V_n_1557] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_1557,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Nat_OSuc(V_n_1557) ),
    inference(cnfTransformation,[status(thm)],[f_3130]) ).

tff(c_3323,plain,
    ~ v_thesis____,
    inference(cnfTransformation,[status(thm)],[f_6032]) ).

tff(c_3321,plain,
    ! [B_t_2799] :
      ( v_thesis____
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t_2799,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____)))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t_2799,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_t_2799) ),
    inference(cnfTransformation,[status(thm)],[f_6030]) ).

tff(c_3324,plain,
    ! [B_t_2799] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t_2799,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____)))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t_2799,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_t_2799) ),
    inference(negUnitSimplification,[status(thm)],[c_3323,c_3321]) ).

tff(c_3343,plain,
    ! [B_t_2799] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t_2799,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____)))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t_2799,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_t_2799) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1727,c_3324]) ).

tff(c_3470,plain,
    ! [B_t_2799] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t_2799,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____)))))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_t_2799,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_t_2799) ),
    inference(demodulation,[status(thm),theory(equality)],[c_68,c_3343]) ).

tff(c_51261,plain,
    ! [V_y_3832] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_3832,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_3832)
      | c_Orderings_Oord__class_Oless(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____)))),V_y_3832)
      | ( 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____)))) = V_y_3832 )
      | ~ class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
    inference(resolution,[status(thm)],[c_51042,c_3470]) ).

tff(c_51579,plain,
    ! [V_y_3832] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_3832,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_3832)
      | c_Orderings_Oord__class_Oless(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____)))),V_y_3832)
      | ( 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____)))) = V_y_3832 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3075,c_51261]) ).

tff(c_92565,plain,
    ! [T_a_113848,V_x_113849,V_z_113850,V_y_113851] :
      ( c_Orderings_Oord__class_Oless(T_a_113848,V_x_113849,V_z_113850)
      | ~ c_Orderings_Oord__class_Oless(T_a_113848,V_y_113851,V_z_113850)
      | ~ c_Orderings_Oord__class_Oless(T_a_113848,V_x_113849,V_y_113851)
      | ~ class_Orderings_Opreorder(T_a_113848) ),
    inference(cnfTransformation,[status(thm)],[f_4740]) ).

tff(c_92605,plain,
    ! [V_x_113849,V_y_3832] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_113849,V_y_3832)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_113849,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____)))))
      | ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_3832,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_3832)
      | ( 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____)))) = V_y_3832 ) ),
    inference(resolution,[status(thm)],[c_51579,c_92565]) ).

tff(c_93323,plain,
    ! [V_x_114265,V_y_114266] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_114265,V_y_114266)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_114265,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____)))))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_114266,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_114266)
      | ( 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____)))) = V_y_114266 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3091,c_92605]) ).

tff(c_93326,plain,
    ! [V_y_114266] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(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____))))),V_y_114266)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_114266,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_114266)
      | ( 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____)))) = V_y_114266 )
      | ~ 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____)))))
      | ~ class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ),
    inference(resolution,[status(thm)],[c_682,c_93323]) ).

tff(c_93358,plain,
    ! [V_y_114266] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(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____))))),V_y_114266)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_114266,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y_114266)
      | ( 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____)))) = V_y_114266 )
      | ~ 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_3031,c_93326]) ).

tff(c_96144,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(splitLeft,[status(thm)],[c_93358]) ).

tff(c_12,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_43]) ).

tff(c_3473,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_68,c_1727,c_12]) ).

tff(c_399404,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_96144,c_3473]) ).

tff(c_399406,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(splitRight,[status(thm)],[c_93358]) ).

tff(c_6,plain,
    ! [V_d2_4] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,'#skF_2'(V_d2_4),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2_4) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_8,plain,
    ! [V_d2_4] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),'#skF_2'(V_d2_4))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2_4) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_4,plain,
    ! [V_d2_4] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,'#skF_2'(V_d2_4),V_d2_4)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2_4) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_399633,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,'#skF_2'(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____))))),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(resolution,[status(thm)],[c_399406,c_4]) ).

tff(c_406788,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,'#skF_2'(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____))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),'#skF_2'(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(resolution,[status(thm)],[c_399633,c_3470]) ).

tff(c_407130,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),'#skF_2'(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(splitLeft,[status(thm)],[c_406788]) ).

tff(c_407559,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(resolution,[status(thm)],[c_8,c_407130]) ).

tff(c_407566,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_399406,c_407559]) ).

tff(c_407567,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,'#skF_2'(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____))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(splitRight,[status(thm)],[c_406788]) ).

tff(c_408004,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(resolution,[status(thm)],[c_6,c_407567]) ).

tff(c_408026,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_399406,c_408004]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWW259+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34  % Computer : n004.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 19:18:56 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 223.27/185.33  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 223.27/185.34  
% 223.27/185.34  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 223.36/185.37  
% 223.36/185.37  Inference rules
% 223.36/185.37  ----------------------
% 223.36/185.37  #Ref     : 152
% 223.36/185.37  #Sup     : 83657
% 223.36/185.37  #Fact    : 16
% 223.36/185.37  #Define  : 0
% 223.36/185.37  #Split   : 111
% 223.36/185.37  #Chain   : 0
% 223.36/185.37  #Close   : 0
% 223.36/185.37  
% 223.36/185.37  Ordering : KBO
% 223.36/185.37  
% 223.36/185.37  Simplification rules
% 223.36/185.37  ----------------------
% 223.36/185.37  #Subsume      : 30605
% 223.36/185.37  #Demod        : 50063
% 223.36/185.37  #Tautology    : 13782
% 223.36/185.37  #SimpNegUnit  : 3403
% 223.36/185.37  #BackRed      : 17
% 223.36/185.37  
% 223.36/185.37  #Partial instantiations: 158436
% 223.36/185.37  #Strategies tried      : 1
% 223.36/185.37  
% 223.36/185.37  Timing (in seconds)
% 223.36/185.37  ----------------------
% 223.36/185.38  Preprocessing        : 2.42
% 223.36/185.38  Parsing              : 1.33
% 223.36/185.38  CNF conversion       : 0.19
% 223.36/185.38  Main loop            : 181.85
% 223.36/185.38  Inferencing          : 17.16
% 223.36/185.38  Reduction            : 104.12
% 223.36/185.38  Demodulation         : 81.30
% 223.36/185.38  BG Simplification    : 0.66
% 223.36/185.38  Subsumption          : 48.90
% 223.36/185.38  Abstraction          : 0.92
% 223.36/185.38  MUC search           : 0.00
% 223.36/185.38  Cooper               : 0.00
% 223.36/185.38  Total                : 184.34
% 223.36/185.38  Index Insertion      : 0.00
% 223.36/185.38  Index Deletion       : 0.00
% 223.36/185.38  Index Matching       : 0.00
% 223.36/185.38  BG Taut test         : 0.00
%------------------------------------------------------------------------------