TSTP Solution File: ALG406-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ALG406-1 : TPTP v8.1.2. Released v4.1.0.
% 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 : n028.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 10:32:41 EDT 2023

% Result   : Unsatisfiable 58.09s 40.30s
% Output   : CNFRefutation 58.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :  123
% Syntax   : Number of formulae    :  188 (  46 unt;  90 typ;   0 def)
%            Number of atoms       :  184 (  36 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :  181 (  95   ~;  86   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  109 (  85   >;  24   *;   0   +;   0  <<)
%            Number of predicates  :   64 (  62 usr;   1 prp; 0-3 aty)
%            Number of functors    :   28 (  28 usr;   5 con; 0-3 aty)
%            Number of variables   :  112 (; 112   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_lessequals > c_HOL_Oord__class_Oless > class_Ring__and__Field_Ozero__neq__one > class_Ring__and__Field_Osemiring > class_Ring__and__Field_Oring__no__zero__divisors > class_Ring__and__Field_Oring__1__no__zero__divisors > class_Ring__and__Field_Oring__1 > class_Ring__and__Field_Oring > class_Ring__and__Field_Opordered__semiring > class_Ring__and__Field_Opordered__ring__abs > class_Ring__and__Field_Opordered__ring > class_Ring__and__Field_Opordered__cancel__semiring > class_Ring__and__Field_Oordered__semiring__strict > class_Ring__and__Field_Oordered__semiring > class_Ring__and__Field_Oordered__semidom > class_Ring__and__Field_Oordered__ring__strict > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Oordered__field > class_Ring__and__Field_Oordered__comm__semiring__strict > class_Ring__and__Field_Ono__zero__divisors > class_Ring__and__Field_Omult__zero > class_Ring__and__Field_Omult__mono1 > class_Ring__and__Field_Omult__mono > class_Ring__and__Field_Olordered__ring > class_Ring__and__Field_Oidom > class_Ring__and__Field_Ofield > class_Ring__and__Field_Odivision__ring > class_Ring__and__Field_Odivision__by__zero > class_Ring__and__Field_Ocomm__semiring__1 > class_Ring__and__Field_Ocomm__semiring > class_Ring__and__Field_Oabs__if > class_RealVector_Oreal__normed__vector > class_RealVector_Oreal__normed__div__algebra > class_RealVector_Oreal__normed__algebra__1 > class_RealVector_Oreal__normed__algebra > class_RealVector_Oreal__algebra__1 > class_Power_Opower > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_OrderedGroup_Opordered__comm__monoid__add > class_OrderedGroup_Opordered__cancel__ab__semigroup__add > class_OrderedGroup_Opordered__ab__semigroup__add__imp__le > class_OrderedGroup_Opordered__ab__semigroup__add > class_OrderedGroup_Opordered__ab__group__add__abs > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Oordered__ab__group__add > class_OrderedGroup_Omonoid__mult > class_OrderedGroup_Omonoid__add > class_OrderedGroup_Olordered__ab__group__add__abs > class_OrderedGroup_Olordered__ab__group__add > class_OrderedGroup_Ogroup__add > class_OrderedGroup_Ocomm__monoid__mult > class_OrderedGroup_Ocomm__monoid__add > class_OrderedGroup_Ocancel__semigroup__add > class_OrderedGroup_Ocancel__ab__semigroup__add > class_OrderedGroup_Oab__semigroup__mult > class_OrderedGroup_Oab__semigroup__idem__mult > class_OrderedGroup_Oab__semigroup__add > class_OrderedGroup_Oab__group__add > class_Lattices_Oboolean__algebra > class_Int_Onumber__ring > c_Power_Opower__class_Opower > c_HOL_Otimes__class_Otimes > c_HOL_Oplus__class_Oplus > c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1 > c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1 > c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1 > c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1 > c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1 > c_RealVector_Osko__RealVector__Xmult__left__Xbounded__1__1 > c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1 > c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1 > c_RealVector_Osko__RealVector__Xmult__Xbounded__1__1 > c_RealVector_Oof__real > c_RealVector_Onorm__class_Onorm > c_HOL_Ouminus__class_Ouminus > c_HOL_Oinverse__class_Oinverse > c_HOL_Oabs__class_Oabs > #nlpp > c_Transcendental_Osin > c_Transcendental_Ocos > c_NthRoot_Osqrt > c_HOL_Ozero__class_Ozero > c_HOL_Oone__class_Oone > c_Complex_ORe > v_w____ > v_t____ > tc_nat > tc_RealDef_Oreal > tc_Complex_Ocomplex

%Foreground sorts:

%Background operators:

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

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

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

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

tff(c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1,type,
    c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1: ( $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

tff(class_Ring__and__Field_Oring__1__no__zero__divisors,type,
    class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).

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

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

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

tff(c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1,type,
    c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1: ( $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1,type,
    c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1: ( $i * $i ) > $i ).

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

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

tff(c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1,type,
    c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1: ( $i * $i ) > $i ).

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

tff(c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1,type,
    c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1: ( $i * $i ) > $i ).

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

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

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

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

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

tff(tc_nat,type,
    tc_nat: $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_OrderedGroup_Opordered__cancel__ab__semigroup__add,type,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).

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

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

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

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

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

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

tff(c_RealVector_Osko__RealVector__Xmult__Xbounded__1__1,type,
    c_RealVector_Osko__RealVector__Xmult__Xbounded__1__1: ( $i * $i ) > $i ).

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

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

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

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

tff(class_RealVector_Oreal__algebra__1,type,
    class_RealVector_Oreal__algebra__1: $i > $o ).

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

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

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

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

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

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

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

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

tff(c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1,type,
    c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1: ( $i * $i ) > $i ).

tff(c_RealVector_Osko__RealVector__Xmult__left__Xbounded__1__1,type,
    c_RealVector_Osko__RealVector__Xmult__left__Xbounded__1__1: ( $i * $i ) > $i ).

tff(class_Ring__and__Field_Omult__mono1,type,
    class_Ring__and__Field_Omult__mono1: $i > $o ).

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

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

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

tff(class_Ring__and__Field_Oring__1,type,
    class_Ring__and__Field_Oring__1: $i > $o ).

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

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

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

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

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

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

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

tff(class_Ring__and__Field_Ocomm__semiring__1,type,
    class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).

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

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

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

tff(c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1,type,
    c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1: ( $i * $i ) > $i ).

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

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

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

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

tff(f_4398,axiom,
    class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
    file(unknown,unknown) ).

tff(f_4120,axiom,
    ! [V_w,V_z] :
      ( c_lessequals(V_w,V_z,tc_RealDef_Oreal)
      | c_lessequals(V_z,V_w,tc_RealDef_Oreal) ),
    file(unknown,unknown) ).

tff(f_4414,axiom,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    file(unknown,unknown) ).

tff(f_4415,axiom,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    file(unknown,unknown) ).

tff(f_4032,axiom,
    c_HOL_Oord__class_Oless(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
    file(unknown,unknown) ).

tff(f_923,axiom,
    ! [T_a,V_z,V_x,V_y] :
      ( ~ class_Orderings_Oorder(T_a)
      | c_HOL_Oord__class_Oless(V_z,V_x,T_a)
      | ~ c_lessequals(V_z,V_y,T_a)
      | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ),
    file(unknown,unknown) ).

tff(f_3240,axiom,
    ! [T_a,V_x] :
      ( ~ class_Orderings_Olinorder(T_a)
      | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ),
    file(unknown,unknown) ).

tff(f_4127,axiom,
    ! [T_a,V_y,V_x] :
      ( ~ class_Orderings_Olinorder(T_a)
      | c_lessequals(V_y,V_x,T_a)
      | c_lessequals(V_x,V_y,T_a) ),
    file(unknown,unknown) ).

tff(f_4413,axiom,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    file(unknown,unknown) ).

tff(f_203,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal),
    file(unknown,unknown) ).

tff(f_956,axiom,
    ! [T_a,V_x,V_z,V_y] :
      ( ~ class_Orderings_Opreorder(T_a)
      | c_HOL_Oord__class_Oless(V_x,V_z,T_a)
      | ~ c_lessequals(V_y,V_z,T_a)
      | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ),
    file(unknown,unknown) ).

tff(f_4409,axiom,
    class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
    file(unknown,unknown) ).

tff(f_1924,axiom,
    c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
    file(unknown,unknown) ).

tff(f_3427,axiom,
    ! [T_a,V_a] :
      ( ~ class_Ring__and__Field_Oabs__if(T_a)
      | ( c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a )
      | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ),
    file(unknown,unknown) ).

tff(f_1488,axiom,
    ! [V_x] :
      ( ( c_NthRoot_Osqrt(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ),
    file(unknown,unknown) ).

tff(f_4407,axiom,
    class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
    file(unknown,unknown) ).

tff(f_4406,axiom,
    class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
    file(unknown,unknown) ).

tff(f_4396,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
    file(unknown,unknown) ).

tff(f_3108,axiom,
    ! [T_a,V_a,V_b] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
      | ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ),
    file(unknown,unknown) ).

tff(f_800,axiom,
    ! [T_a,V_a] :
      ( ~ class_OrderedGroup_Omonoid__add(T_a)
      | ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ),
    file(unknown,unknown) ).

tff(f_3178,axiom,
    ! [T_a,V_a,V_b] :
      ( ~ class_OrderedGroup_Ogroup__add(T_a)
      | ( c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a) )
      | ( c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) ),
    file(unknown,unknown) ).

tff(f_858,axiom,
    ! [T_a,V_a] :
      ( ~ class_OrderedGroup_Ogroup__add(T_a)
      | ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = V_a ) ),
    file(unknown,unknown) ).

tff(f_4367,axiom,
    class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
    file(unknown,unknown) ).

tff(f_1997,axiom,
    ! [T_a,V_a] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
      | ( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_a,T_a) ) ),
    file(unknown,unknown) ).

tff(f_4151,axiom,
    ! [V_w] : c_lessequals(V_w,V_w,tc_RealDef_Oreal),
    file(unknown,unknown) ).

tff(f_1161,axiom,
    ! [T_a,V_a,V_b] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
      | c_lessequals(V_a,V_b,T_a)
      | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ),
    file(unknown,unknown) ).

tff(f_1225,axiom,
    ! [T_a,V_x,V_y] :
      ( ~ class_Orderings_Olinorder(T_a)
      | ~ c_lessequals(V_x,V_y,T_a)
      | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ),
    file(unknown,unknown) ).

tff(f_4376,axiom,
    class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
    file(unknown,unknown) ).

tff(f_4029,axiom,
    ! [V_x] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(V_x,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,tc_Complex_Ocomplex),tc_RealDef_Oreal),
    file(unknown,unknown) ).

tff(f_3069,axiom,
    ! [T_a,V_a] :
      ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
      | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
      | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) ),
    file(unknown,unknown) ).

tff(f_4060,axiom,
    ! [T_a,V_y,V_x] :
      ( ~ class_Ring__and__Field_Oordered__idom(T_a)
      | c_lessequals(c_HOL_Otimes__class_Otimes(V_y,V_x,T_a),V_x,T_a)
      | ~ c_lessequals(V_y,c_HOL_Oone__class_Oone(T_a),T_a)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ),
    file(unknown,unknown) ).

tff(f_4304,axiom,
    ! [V_z] : ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) = V_z ),
    file(unknown,unknown) ).

tff(f_4329,axiom,
    ~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
    file(unknown,unknown) ).

tff(c_1256,plain,
    class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_4398]) ).

tff(c_1042,plain,
    ! [V_z_1386,V_w_1385] :
      ( c_lessequals(V_z_1386,V_w_1385,tc_RealDef_Oreal)
      | c_lessequals(V_w_1385,V_z_1386,tc_RealDef_Oreal) ),
    inference(cnfTransformation,[status(thm)],[f_4120]) ).

tff(c_1288,plain,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_4414]) ).

tff(c_1290,plain,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_4415]) ).

tff(c_1016,plain,
    c_HOL_Oord__class_Oless(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_4032]) ).

tff(c_36741,plain,
    ! [V_y_2137,V_x_2138,T_a_2139,V_z_2140] :
      ( ~ c_HOL_Oord__class_Oless(V_y_2137,V_x_2138,T_a_2139)
      | ~ c_lessequals(V_z_2140,V_y_2137,T_a_2139)
      | c_HOL_Oord__class_Oless(V_z_2140,V_x_2138,T_a_2139)
      | ~ class_Orderings_Oorder(T_a_2139) ),
    inference(cnfTransformation,[status(thm)],[f_923]) ).

tff(c_36811,plain,
    ! [V_z_2140] :
      ( ~ c_lessequals(V_z_2140,v_t____,tc_RealDef_Oreal)
      | c_HOL_Oord__class_Oless(V_z_2140,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
      | ~ class_Orderings_Oorder(tc_RealDef_Oreal) ),
    inference(resolution,[status(thm)],[c_1016,c_36741]) ).

tff(c_48213,plain,
    ! [V_z_2298] :
      ( ~ c_lessequals(V_z_2298,v_t____,tc_RealDef_Oreal)
      | c_HOL_Oord__class_Oless(V_z_2298,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1290,c_36811]) ).

tff(c_810,plain,
    ! [V_x_1090,T_a_1089] :
      ( ~ c_HOL_Oord__class_Oless(V_x_1090,V_x_1090,T_a_1089)
      | ~ class_Orderings_Olinorder(T_a_1089) ),
    inference(cnfTransformation,[status(thm)],[f_3240]) ).

tff(c_48291,plain,
    ( ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal) ),
    inference(resolution,[status(thm)],[c_48213,c_810]) ).

tff(c_48363,plain,
    ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal),
    inference(demodulation,[status(thm),theory(equality)],[c_1288,c_48291]) ).

tff(c_48431,plain,
    c_lessequals(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(resolution,[status(thm)],[c_1042,c_48363]) ).

tff(c_1044,plain,
    ! [V_x_1389,V_y_1388,T_a_1387] :
      ( c_lessequals(V_x_1389,V_y_1388,T_a_1387)
      | c_lessequals(V_y_1388,V_x_1389,T_a_1387)
      | ~ class_Orderings_Olinorder(T_a_1387) ),
    inference(cnfTransformation,[status(thm)],[f_4127]) ).

tff(c_1286,plain,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_4413]) ).

tff(c_54,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_203]) ).

tff(c_36328,plain,
    ! [V_x_2132,V_y_2133,T_a_2134,V_z_2135] :
      ( ~ c_HOL_Oord__class_Oless(V_x_2132,V_y_2133,T_a_2134)
      | ~ c_lessequals(V_y_2133,V_z_2135,T_a_2134)
      | c_HOL_Oord__class_Oless(V_x_2132,V_z_2135,T_a_2134)
      | ~ class_Orderings_Opreorder(T_a_2134) ),
    inference(cnfTransformation,[status(thm)],[f_956]) ).

tff(c_36400,plain,
    ! [V_z_2135] :
      ( ~ c_lessequals(v_t____,V_z_2135,tc_RealDef_Oreal)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2135,tc_RealDef_Oreal)
      | ~ class_Orderings_Opreorder(tc_RealDef_Oreal) ),
    inference(resolution,[status(thm)],[c_54,c_36328]) ).

tff(c_43303,plain,
    ! [V_z_2231] :
      ( ~ c_lessequals(v_t____,V_z_2231,tc_RealDef_Oreal)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2231,tc_RealDef_Oreal) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1286,c_36400]) ).

tff(c_1278,plain,
    class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_4409]) ).

tff(c_454,plain,
    c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_1924]) ).

tff(c_9241,plain,
    ! [V_a_1744,T_a_1745] :
      ( c_HOL_Oord__class_Oless(V_a_1744,c_HOL_Ozero__class_Ozero(T_a_1745),T_a_1745)
      | ( c_HOL_Oabs__class_Oabs(V_a_1744,T_a_1745) = V_a_1744 )
      | ~ class_Ring__and__Field_Oabs__if(T_a_1745) ),
    inference(cnfTransformation,[status(thm)],[f_3427]) ).

tff(c_348,plain,
    ! [V_x_496] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_496,tc_RealDef_Oreal)
      | ( c_NthRoot_Osqrt(V_x_496) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(cnfTransformation,[status(thm)],[f_1488]) ).

tff(c_9261,plain,
    ( ( c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
    | ( c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
    | ~ class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) ),
    inference(resolution,[status(thm)],[c_9241,c_348]) ).

tff(c_9302,plain,
    c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(demodulation,[status(thm),theory(equality)],[c_1278,c_454,c_9261]) ).

tff(c_1274,plain,
    class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_4407]) ).

tff(c_1272,plain,
    class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_4406]) ).

tff(c_1252,plain,
    class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_4396]) ).

tff(c_4604,plain,
    ! [V_b_1646,V_a_1647,T_a_1648] :
      ( ( c_HOL_Oplus__class_Oplus(V_b_1646,V_a_1647,T_a_1648) = c_HOL_Oplus__class_Oplus(V_a_1647,V_b_1646,T_a_1648) )
      | ~ class_OrderedGroup_Ocomm__monoid__add(T_a_1648) ),
    inference(cnfTransformation,[status(thm)],[f_3108]) ).

tff(c_6515,plain,
    ! [V_b_1692,V_a_1693] : ( c_HOL_Oplus__class_Oplus(V_b_1692,V_a_1693,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(V_a_1693,V_b_1692,tc_RealDef_Oreal) ),
    inference(resolution,[status(thm)],[c_1252,c_4604]) ).

tff(c_188,plain,
    ! [T_a_255,V_a_256] :
      ( ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a_255),V_a_256,T_a_255) = V_a_256 )
      | ~ class_OrderedGroup_Omonoid__add(T_a_255) ),
    inference(cnfTransformation,[status(thm)],[f_800]) ).

tff(c_6563,plain,
    ! [V_b_1692] :
      ( ( c_HOL_Oplus__class_Oplus(V_b_1692,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = V_b_1692 )
      | ~ class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_6515,c_188]) ).

tff(c_6713,plain,
    ! [V_b_1692] : ( c_HOL_Oplus__class_Oplus(V_b_1692,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = V_b_1692 ),
    inference(demodulation,[status(thm),theory(equality)],[c_1272,c_6563]) ).

tff(c_17805,plain,
    ! [V_a_1888,T_a_1889,V_b_1890] :
      ( ( c_HOL_Ouminus__class_Ouminus(V_a_1888,T_a_1889) = V_b_1890 )
      | ( c_HOL_Oplus__class_Oplus(V_a_1888,V_b_1890,T_a_1889) != c_HOL_Ozero__class_Ozero(T_a_1889) )
      | ~ class_OrderedGroup_Ogroup__add(T_a_1889) ),
    inference(cnfTransformation,[status(thm)],[f_3178]) ).

tff(c_17831,plain,
    ! [V_b_1692] :
      ( ( c_HOL_Ouminus__class_Ouminus(V_b_1692,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_b_1692 )
      | ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_6713,c_17805]) ).

tff(c_18038,plain,
    ! [V_b_1892] :
      ( ( c_HOL_Ouminus__class_Ouminus(V_b_1892,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
      | ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_b_1892 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1274,c_17831]) ).

tff(c_210,plain,
    ! [V_a_278,T_a_277] :
      ( ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a_278,T_a_277),T_a_277) = V_a_278 )
      | ~ class_OrderedGroup_Ogroup__add(T_a_277) ),
    inference(cnfTransformation,[status(thm)],[f_858]) ).

tff(c_1194,plain,
    class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_4367]) ).

tff(c_474,plain,
    ! [V_a_649,T_a_648] :
      ( ( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a_649,T_a_648),T_a_648) = c_HOL_Oabs__class_Oabs(V_a_649,T_a_648) )
      | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a_648) ),
    inference(cnfTransformation,[status(thm)],[f_1997]) ).

tff(c_1050,plain,
    ! [V_w_1398] : c_lessequals(V_w_1398,V_w_1398,tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_4151]) ).

tff(c_14071,plain,
    ! [V_a_1826,T_a_1827,V_b_1828] :
      ( ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a_1826,T_a_1827),V_b_1828,T_a_1827)
      | c_lessequals(V_a_1826,V_b_1828,T_a_1827)
      | ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a_1827) ),
    inference(cnfTransformation,[status(thm)],[f_1161]) ).

tff(c_14147,plain,
    ! [V_a_1826] :
      ( c_lessequals(V_a_1826,c_HOL_Oabs__class_Oabs(V_a_1826,tc_RealDef_Oreal),tc_RealDef_Oreal)
      | ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
    inference(resolution,[status(thm)],[c_1050,c_14071]) ).

tff(c_14176,plain,
    ! [V_a_1829] : c_lessequals(V_a_1829,c_HOL_Oabs__class_Oabs(V_a_1829,tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(demodulation,[status(thm),theory(equality)],[c_1194,c_14147]) ).

tff(c_14211,plain,
    ! [V_a_649] :
      ( c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a_649,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(V_a_649,tc_RealDef_Oreal),tc_RealDef_Oreal)
      | ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_474,c_14176]) ).

tff(c_14450,plain,
    ! [V_a_1834] : c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a_1834,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(V_a_1834,tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(demodulation,[status(thm),theory(equality)],[c_1194,c_14211]) ).

tff(c_14517,plain,
    ! [V_a_278] :
      ( c_lessequals(V_a_278,c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a_278,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
      | ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
    inference(superposition,[status(thm),theory(equality)],[c_210,c_14450]) ).

tff(c_14545,plain,
    ! [V_a_278] : c_lessequals(V_a_278,c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a_278,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(demodulation,[status(thm),theory(equality)],[c_1274,c_14517]) ).

tff(c_18047,plain,
    ! [V_b_1892] :
      ( c_lessequals(V_b_1892,c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
      | ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_b_1892 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_18038,c_14545]) ).

tff(c_32173,plain,
    ! [V_b_2071] :
      ( c_lessequals(V_b_2071,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
      | ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_b_2071 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_9302,c_18047]) ).

tff(c_292,plain,
    ! [V_y_416,V_x_415,T_a_414] :
      ( ~ c_HOL_Oord__class_Oless(V_y_416,V_x_415,T_a_414)
      | ~ c_lessequals(V_x_415,V_y_416,T_a_414)
      | ~ class_Orderings_Olinorder(T_a_414) ),
    inference(cnfTransformation,[status(thm)],[f_1225]) ).

tff(c_32232,plain,
    ! [V_b_2071] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_b_2071,tc_RealDef_Oreal)
      | ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
      | ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_b_2071 ) ),
    inference(resolution,[status(thm)],[c_32173,c_292]) ).

tff(c_32291,plain,
    ! [V_b_2071] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_b_2071,tc_RealDef_Oreal)
      | ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_b_2071 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1288,c_32232]) ).

tff(c_43650,plain,
    ! [V_z_2235] :
      ( ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_z_2235 )
      | ~ c_lessequals(v_t____,V_z_2235,tc_RealDef_Oreal) ),
    inference(resolution,[status(thm)],[c_43303,c_32291]) ).

tff(c_43690,plain,
    ! [V_y_1388] :
      ( ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != V_y_1388 )
      | c_lessequals(V_y_1388,v_t____,tc_RealDef_Oreal)
      | ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
    inference(resolution,[status(thm)],[c_1044,c_43650]) ).

tff(c_43775,plain,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal),
    inference(demodulation,[status(thm),theory(equality)],[c_1288,c_43690]) ).

tff(c_1212,plain,
    class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_4376]) ).

tff(c_1012,plain,
    ! [V_x_1342] : c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(V_x_1342,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x_1342,tc_Complex_Ocomplex),tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_4029]) ).

tff(c_23744,plain,
    ! [V_a_1973,T_a_1974] :
      ( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a_1973,T_a_1974),V_a_1973,T_a_1974)
      | c_lessequals(c_HOL_Ozero__class_Ozero(T_a_1974),V_a_1973,T_a_1974)
      | ~ class_OrderedGroup_Oordered__ab__group__add(T_a_1974) ),
    inference(cnfTransformation,[status(thm)],[f_3069]) ).

tff(c_23784,plain,
    ! [V_x_1342] :
      ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x_1342,tc_Complex_Ocomplex),tc_RealDef_Oreal)
      | ~ class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ),
    inference(resolution,[status(thm)],[c_1012,c_23744]) ).

tff(c_23856,plain,
    ! [V_x_1342] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x_1342,tc_Complex_Ocomplex),tc_RealDef_Oreal),
    inference(demodulation,[status(thm),theory(equality)],[c_1212,c_23784]) ).

tff(c_162384,plain,
    ! [T_a_3101,V_x_3102,V_y_3103] :
      ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a_3101),V_x_3102,T_a_3101)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a_3101),V_y_3103,T_a_3101)
      | ~ c_lessequals(V_y_3103,c_HOL_Oone__class_Oone(T_a_3101),T_a_3101)
      | c_lessequals(c_HOL_Otimes__class_Otimes(V_y_3103,V_x_3102,T_a_3101),V_x_3102,T_a_3101)
      | ~ class_Ring__and__Field_Oordered__idom(T_a_3101) ),
    inference(cnfTransformation,[status(thm)],[f_4060]) ).

tff(c_1104,plain,
    ! [V_z_1479] : ( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_z_1479,tc_RealDef_Oreal) = V_z_1479 ),
    inference(cnfTransformation,[status(thm)],[f_4304]) ).

tff(c_1118,plain,
    ~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_4329]) ).

tff(c_1357,plain,
    ~ c_lessequals(c_HOL_Otimes__class_Otimes(v_t____,c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
    inference(demodulation,[status(thm),theory(equality)],[c_1104,c_1118]) ).

tff(c_162466,plain,
    ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal)
    | ~ c_lessequals(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ),
    inference(resolution,[status(thm)],[c_162384,c_1357]) ).

tff(c_162720,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1256,c_48431,c_43775,c_23856,c_162466]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : ALG406-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.15  % 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
% 0.15/0.36  % Computer : n028.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 20:27:54 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 58.09/40.30  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 58.09/40.31  
% 58.09/40.31  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 58.09/40.35  
% 58.09/40.35  Inference rules
% 58.09/40.35  ----------------------
% 58.09/40.35  #Ref     : 24
% 58.09/40.35  #Sup     : 36866
% 58.09/40.35  #Fact    : 8
% 58.09/40.35  #Define  : 0
% 58.09/40.35  #Split   : 12
% 58.09/40.35  #Chain   : 0
% 58.09/40.35  #Close   : 0
% 58.09/40.36  
% 58.09/40.36  Ordering : KBO
% 58.09/40.36  
% 58.09/40.36  Simplification rules
% 58.09/40.36  ----------------------
% 58.09/40.36  #Subsume      : 6184
% 58.09/40.36  #Demod        : 23094
% 58.09/40.36  #Tautology    : 6168
% 58.09/40.36  #SimpNegUnit  : 717
% 58.09/40.36  #BackRed      : 5
% 58.09/40.36  
% 58.09/40.36  #Partial instantiations: 0
% 58.09/40.36  #Strategies tried      : 1
% 58.09/40.36  
% 58.09/40.36  Timing (in seconds)
% 58.09/40.36  ----------------------
% 58.09/40.36  Preprocessing        : 1.50
% 58.09/40.36  Parsing              : 0.87
% 58.09/40.36  CNF conversion       : 0.13
% 58.09/40.36  Main loop            : 37.77
% 58.09/40.36  Inferencing          : 4.38
% 58.09/40.36  Reduction            : 20.34
% 58.09/40.36  Demodulation         : 16.53
% 58.09/40.36  BG Simplification    : 0.44
% 58.09/40.36  Subsumption          : 10.45
% 58.09/40.36  Abstraction          : 0.43
% 58.09/40.36  MUC search           : 0.00
% 58.09/40.36  Cooper               : 0.00
% 58.09/40.36  Total                : 39.35
% 58.09/40.36  Index Insertion      : 0.00
% 58.09/40.36  Index Deletion       : 0.00
% 58.09/40.36  Index Matching       : 0.00
% 58.09/40.36  BG Taut test         : 0.00
%------------------------------------------------------------------------------