TSTP Solution File: ALG387-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ALG387-1 : 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/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 : n031.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 10:32:39 EDT 2023

% Result   : Unsatisfiable 140.48s 111.16s
% Output   : CNFRefutation 140.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :  116
% Syntax   : Number of formulae    :  128 (   8 unt; 110 typ;   0 def)
%            Number of atoms       :   31 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   26 (  13   ~;  13   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  143 ( 102   >;  41   *;   0   +;   0  <<)
%            Number of predicates  :   72 (  71 usr;   1 prp; 0-3 aty)
%            Number of functors    :   39 (  39 usr;   8 con; 0-3 aty)
%            Number of variables   :   20 (;  20   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_lessequals > c_HOL_Oord__class_Oless > c_HOL_Oeq__class_Oeq > c_Polynomial_Opos__poly > class_SEQ_Obanach > 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 > 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__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_Ocomm__semiring__1 > class_Ring__and__Field_Ocomm__semiring__0 > class_Ring__and__Field_Ocomm__semiring > class_Ring__and__Field_Ocomm__ring__1 > class_Ring__and__Field_Ocomm__ring > class_Ring__and__Field_Oabs__if > class_RealVector_Oreal__normed__vector > class_RealVector_Oreal__normed__field > 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_Olinorder > class_Orderings_Obot > 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__meet > 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__comm__monoid__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_Olower__semilattice > class_Lattices_Olattice > class_Lattices_Obounded__lattice > class_Lattices_Oboolean__algebra > class_Int_Onumber__ring > class_HOL_Ozero > class_HOL_Oeq > v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1 > c_Power_Opower__class_Opower > c_Polynomial_Osynthetic__div > c_Polynomial_Osmult > c_Polynomial_Opoly > c_Polynomial_Opcompose > c_Polynomial_OpCons > c_Orderings_Oord__class_Omin > c_Orderings_Oord__class_Omax > c_Lattices_Olower__semilattice__class_Oinf > c_HOL_Otimes__class_Otimes > c_HOL_Oplus__class_Oplus > c_HOL_Ominus__class_Ominus > v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__disc__1 > v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1 > hAPP > c_Transcendental_Oexp > c_RealVector_Onorm__class_Onorm > c_HOL_Ouminus__class_Ouminus > c_HOL_Oabs__class_Oabs > c_Fun_Oid > #nlpp > v_sko__local__XpCons__Xhyps__1 > v_sko__local__XpCons__1 > tc_Polynomial_Opoly > c_Transcendental_Oarctan > c_Orderings_Obot__class_Obot > c_NthRoot_Osqrt > c_HOL_Ozero__class_Ozero > c_Complex_Ocnj > c_Complex_ORe > c_Complex_OIm > v_x > v_v____ > v_r____ > v_cs____ > v_c____ > tc_RealDef_Oreal > tc_Complex_Ocomplex > t_a

%Foreground sorts:

%Background operators:

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

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

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

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

tff(class_Ring__and__Field_Ocomm__semiring__0,type,
    class_Ring__and__Field_Ocomm__semiring__0: $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(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_Complex_OIm,type,
    c_Complex_OIm: $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(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1,type,
    v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__infinity__1: ( $i * $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

tff(class_OrderedGroup_Olordered__ab__group__add__meet,type,
    class_OrderedGroup_Olordered__ab__group__add__meet: $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(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1,type,
    v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1: ( $i * $i ) > $i ).

tff(class_Ring__and__Field_Ono__zero__divisors,type,
    class_Ring__and__Field_Ono__zero__divisors: $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_Orderings_Obot__class_Obot,type,
    c_Orderings_Obot__class_Obot: $i > $i ).

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

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

tff(c_Orderings_Oord__class_Omin,type,
    c_Orderings_Oord__class_Omin: ( $i * $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_Ocomm__ring__1,type,
    class_Ring__and__Field_Ocomm__ring__1: $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(c_Polynomial_Osmult,type,
    c_Polynomial_Osmult: ( $i * $i * $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_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(c_Orderings_Oord__class_Omax,type,
    c_Orderings_Oord__class_Omax: ( $i * $i * $i ) > $i ).

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

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

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(v_sko__local__XpCons__Xhyps__1,type,
    v_sko__local__XpCons__Xhyps__1: $i > $i ).

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

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

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

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

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

tff(c_Polynomial_OpCons,type,
    c_Polynomial_OpCons: ( $i * $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_Fun_Oid,type,
    c_Fun_Oid: ( $i * $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_OrderedGroup_Olordered__ab__group__add__abs,type,
    class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).

tff(v_sko__local__XpCons__1,type,
    v_sko__local__XpCons__1: $i > $i ).

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(c_Polynomial_Opcompose,type,
    c_Polynomial_Opcompose: ( $i * $i * $i ) > $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_Complex_Ocnj,type,
    c_Complex_Ocnj: $i > $i ).

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

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

tff(c_HOL_Oeq__class_Oeq,type,
    c_HOL_Oeq__class_Oeq: ( $i * $i * $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(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__disc__1,type,
    v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__minimum__modulus__disc__1: ( $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

tff(f_5280,axiom,
    ! [V_z] :
      ( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
      | ~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
    file(unknown,unknown) ).

tff(f_5283,axiom,
    ! [V_xa] : ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),V_xa,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,V_xa),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
    file(unknown,unknown) ).

tff(f_5357,axiom,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    file(unknown,unknown) ).

tff(f_5167,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_4986,axiom,
    ! [V_x,V_r] :
      ( c_lessequals(V_x,V_r,tc_RealDef_Oreal)
      | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),V_r,tc_RealDef_Oreal) ),
    file(unknown,unknown) ).

tff(f_5275,axiom,
    ! [V_w] :
      ( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),V_w,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
      | ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_w,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    file(unknown,unknown) ).

tff(c_336801,plain,
    ! [V_z_5148] :
      ( ~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(V_z_5148,tc_Complex_Ocomplex),tc_RealDef_Oreal)
      | c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),V_z_5148,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
    inference(cnfTransformation,[status(thm)],[f_5280]) ).

tff(c_1472,plain,
    ! [V_xa_2176] : ~ c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),V_xa_2176,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),hAPP(v_x,V_xa_2176),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_5283]) ).

tff(c_336875,plain,
    ~ c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),tc_RealDef_Oreal),
    inference(resolution,[status(thm)],[c_336801,c_1472]) ).

tff(c_1596,plain,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_5357]) ).

tff(c_1440,plain,
    ! [V_x_2135,V_y_2134,T_a_2133] :
      ( c_lessequals(V_x_2135,V_y_2134,T_a_2133)
      | c_lessequals(V_y_2134,V_x_2135,T_a_2133)
      | ~ class_Orderings_Olinorder(T_a_2133) ),
    inference(cnfTransformation,[status(thm)],[f_5167]) ).

tff(c_9313,plain,
    ! [V_x_2622,V_r_2623] :
      ( ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_x_2622,tc_RealDef_Oreal),V_r_2623,tc_RealDef_Oreal)
      | c_lessequals(V_x_2622,V_r_2623,tc_RealDef_Oreal) ),
    inference(cnfTransformation,[status(thm)],[f_4986]) ).

tff(c_9328,plain,
    ! [V_x_2622,V_x_2135] :
      ( c_lessequals(V_x_2622,V_x_2135,tc_RealDef_Oreal)
      | c_lessequals(V_x_2135,c_HOL_Oabs__class_Oabs(V_x_2622,tc_RealDef_Oreal),tc_RealDef_Oreal)
      | ~ class_Orderings_Olinorder(tc_RealDef_Oreal) ),
    inference(resolution,[status(thm)],[c_1440,c_9313]) ).

tff(c_9422,plain,
    ! [V_x_2622,V_x_2135] :
      ( c_lessequals(V_x_2622,V_x_2135,tc_RealDef_Oreal)
      | c_lessequals(V_x_2135,c_HOL_Oabs__class_Oabs(V_x_2622,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1596,c_9328]) ).

tff(c_339995,plain,
    ! [V_w_5160] :
      ( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_w_5160,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),tc_RealDef_Oreal)
      | c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),v_v____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,tc_Complex_Ocomplex),V_w_5160,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
    inference(cnfTransformation,[status(thm)],[f_5275]) ).

tff(c_340069,plain,
    ~ c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(v_r____,tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(resolution,[status(thm)],[c_339995,c_1472]) ).

tff(c_342358,plain,
    c_lessequals(v_r____,c_RealVector_Onorm__class_Onorm(hAPP(v_x,v_v____),tc_Complex_Ocomplex),tc_RealDef_Oreal),
    inference(resolution,[status(thm)],[c_9422,c_340069]) ).

tff(c_342438,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_336875,c_342358]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : ALG387-1 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.14  % 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
% 0.14/0.36  % Computer : n031.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 20:45:15 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 140.48/111.16  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 140.48/111.16  
% 140.48/111.16  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 140.48/111.19  
% 140.48/111.19  Inference rules
% 140.48/111.19  ----------------------
% 140.48/111.19  #Ref     : 52
% 140.48/111.19  #Sup     : 76000
% 140.48/111.19  #Fact    : 28
% 140.48/111.19  #Define  : 0
% 140.48/111.19  #Split   : 6
% 140.48/111.19  #Chain   : 0
% 140.48/111.19  #Close   : 0
% 140.48/111.19  
% 140.48/111.19  Ordering : KBO
% 140.48/111.19  
% 140.48/111.19  Simplification rules
% 140.48/111.19  ----------------------
% 140.48/111.19  #Subsume      : 11025
% 140.48/111.19  #Demod        : 60009
% 140.48/111.19  #Tautology    : 15760
% 140.48/111.19  #SimpNegUnit  : 734
% 140.48/111.19  #BackRed      : 8
% 140.48/111.19  
% 140.48/111.19  #Partial instantiations: 0
% 140.48/111.19  #Strategies tried      : 1
% 140.48/111.19  
% 140.48/111.19  Timing (in seconds)
% 140.48/111.19  ----------------------
% 140.48/111.20  Preprocessing        : 1.70
% 140.48/111.20  Parsing              : 0.96
% 140.48/111.20  CNF conversion       : 0.14
% 140.48/111.20  Main loop            : 108.37
% 140.48/111.20  Inferencing          : 9.24
% 140.48/111.20  Reduction            : 58.07
% 140.48/111.20  Demodulation         : 49.30
% 140.48/111.20  BG Simplification    : 0.96
% 140.48/111.20  Subsumption          : 33.64
% 140.48/111.20  Abstraction          : 1.17
% 140.48/111.20  MUC search           : 0.00
% 140.48/111.20  Cooper               : 0.00
% 140.48/111.20  Total                : 110.12
% 140.48/111.20  Index Insertion      : 0.00
% 140.48/111.20  Index Deletion       : 0.00
% 140.48/111.20  Index Matching       : 0.00
% 140.48/111.20  BG Taut test         : 0.00
%------------------------------------------------------------------------------