TSTP Solution File: ALG361-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ALG361-1 : 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 : n021.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 10:32:36 EDT 2023

% Result   : Unsatisfiable 19.29s 6.17s
% Output   : CNFRefutation 19.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   95
% Syntax   : Number of formulae    :  102 (   8 unt;  91 typ;   0 def)
%            Number of atoms       :   16 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   14 (   9   ~;   5   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  139 (  81   >;  58   *;   0   +;   0  <<)
%            Number of predicates  :   64 (  63 usr;   2 prp; 0-5 aty)
%            Number of functors    :   28 (  28 usr;   9 con; 0-5 aty)
%            Number of variables   :    3 (;   3   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_Limits_Otendsto > c_Lim_OLIM > c_Limits_OZfun > c_Lim_OisCont > c_lessequals > c_fequal > c_Series_Osums > c_SEQ_OLIMSEQ > c_RealVector_Obounded__linear > c_Lim_OisUCont > c_HOL_Oord__class_Oless > c_Deriv_Odifferentiable > c_Series_Osummable > c_SEQ_OZseq > c_SEQ_OCauchy > hBOOL > class_SEQ_Obanach > class_Ring__and__Field_Osemiring__0 > class_Ring__and__Field_Oring__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__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_Oabs__if > class_RealVector_Oreal__vector > class_RealVector_Oreal__normed__vector > class_RealVector_Oreal__normed__field > class_RealVector_Oreal__normed__algebra__1 > class_RealVector_Oreal__normed__algebra > class_RealVector_Oreal__algebra__1 > class_RealVector_Oreal__algebra > class_RealVector_Ometric__space > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_OrderedGroup_Opordered__ab__group__add__abs > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Oordered__ab__group__add > class_OrderedGroup_Olordered__ab__group__add__abs > class_OrderedGroup_Olordered__ab__group__add > class_OrderedGroup_Ogroup__add > class_OrderedGroup_Oab__semigroup__mult > class_OrderedGroup_Oab__semigroup__idem__mult > class_OrderedGroup_Oab__group__add > class_Lattices_Oboolean__algebra > c_SEQ_Osubseq > c_SEQ_Omonoseq > c_SEQ_Oincseq > c_SEQ_Odecseq > c_Fun_Ocomp > c_COMBB > c_Set_Oimage > c_Series_Osko__Series__Xsummable__comparison__test__1__1 > c_Finite__Set_Osetsum > c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1 > tc_fun > hAPP > c_Series_Osuminf > c_RealVector_OscaleR__class_OscaleR > c_HOL_Otimes__class_Otimes > c_Complex_Ocomplex_OComplex > #nlpp > v_sko__CHAINED__1 > c_SEQ_Osko__SEQ__Xseq__monosub__1__1 > c_RealVector_Oof__real > c_RealVector_Onorm__class_Onorm > c_HOL_Ozero__class_Ozero > c_HOL_Ouminus__class_Ouminus > c_HOL_Oabs__class_Oabs > v_z > v_thesis____ > v_s > tc_nat > tc_bool > tc_RealDef_Oreal > tc_Complex_Ocomplex > c_Complex_Ocnj > c_Complex_ORe > c_Complex_OIm

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

tff(c_SEQ_Osko__SEQ__Xseq__monosub__1__1,type,
    c_SEQ_Osko__SEQ__Xseq__monosub__1__1: $i > $i ).

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

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

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

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(class_Ring__and__Field_Osemiring__0,type,
    class_Ring__and__Field_Osemiring__0: $i > $o ).

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

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

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

tff(v_thesis____,type,
    v_thesis____: $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(c_COMBB,type,
    c_COMBB: ( $i * $i * $i * $i * $i ) > $i ).

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

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

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_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(c_Complex_OIm,type,
    c_Complex_OIm: $i ).

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

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_Obounded__linear,type,
    c_RealVector_Obounded__linear: ( $i * $i * $i ) > $o ).

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

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

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

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

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

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

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

tff(c_Deriv_Odifferentiable,type,
    c_Deriv_Odifferentiable: ( $i * $i * $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(tc_bool,type,
    tc_bool: $i ).

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

tff(class_RealVector_Oreal__algebra,type,
    class_RealVector_Oreal__algebra: $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(c_SEQ_Osubseq,type,
    c_SEQ_Osubseq: $i > $o ).

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

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_SEQ_Oincseq,type,
    c_SEQ_Oincseq: $i > $o ).

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

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

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

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

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

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

tff(c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1,type,
    c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1: ( $i * $i * $i ) > $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(c_SEQ_Odecseq,type,
    c_SEQ_Odecseq: $i > $o ).

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

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

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

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

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

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

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

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

tff(v_sko__CHAINED__1,type,
    v_sko__CHAINED__1: $i > $i ).

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

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

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

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

tff(c_Series_Osko__Series__Xsummable__comparison__test__1__1,type,
    c_Series_Osko__Series__Xsummable__comparison__test__1__1: ( $i * $i * $i * $i ) > $i ).

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

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

tff(f_3974,axiom,
    c_SEQ_Osubseq(v_sko__CHAINED__1(v_s)),
    file(unknown,unknown) ).

tff(f_3973,axiom,
    c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)),
    file(unknown,unknown) ).

tff(f_3976,axiom,
    ~ v_thesis____,
    file(unknown,unknown) ).

tff(f_3967,axiom,
    ! [V_f] :
      ( v_thesis____
      | ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat))
      | ~ c_SEQ_Osubseq(V_f) ),
    file(unknown,unknown) ).

tff(c_1024,plain,
    c_SEQ_Osubseq(v_sko__CHAINED__1(v_s)),
    inference(cnfTransformation,[status(thm)],[f_3974]) ).

tff(c_1022,plain,
    c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)),
    inference(cnfTransformation,[status(thm)],[f_3973]) ).

tff(c_1026,plain,
    ~ v_thesis____,
    inference(cnfTransformation,[status(thm)],[f_3976]) ).

tff(c_1018,plain,
    ! [V_f_1533] :
      ( ~ c_SEQ_Osubseq(V_f_1533)
      | ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f_1533,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat))
      | v_thesis____ ),
    inference(cnfTransformation,[status(thm)],[f_3967]) ).

tff(c_18516,plain,
    ! [V_f_2109] :
      ( ~ c_SEQ_Osubseq(V_f_2109)
      | ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,V_f_2109,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) ),
    inference(negUnitSimplification,[status(thm)],[c_1026,c_1018]) ).

tff(c_18519,plain,
    ~ c_SEQ_Osubseq(v_sko__CHAINED__1(v_s)),
    inference(resolution,[status(thm)],[c_1022,c_18516]) ).

tff(c_18529,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1024,c_18519]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : ALG361-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.12  % 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
% 0.13/0.33  % Computer : n021.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Thu Aug  3 20:29:06 EDT 2023
% 0.19/0.33  % CPUTime  : 
% 19.29/6.17  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.29/6.18  
% 19.29/6.18  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 19.64/6.26  
% 19.64/6.26  Inference rules
% 19.64/6.26  ----------------------
% 19.64/6.26  #Ref     : 18
% 19.64/6.26  #Sup     : 3787
% 19.64/6.26  #Fact    : 14
% 19.64/6.26  #Define  : 0
% 19.64/6.26  #Split   : 11
% 19.64/6.26  #Chain   : 0
% 19.64/6.26  #Close   : 0
% 19.64/6.26  
% 19.64/6.26  Ordering : KBO
% 19.64/6.26  
% 19.64/6.26  Simplification rules
% 19.64/6.26  ----------------------
% 19.64/6.26  #Subsume      : 1277
% 19.64/6.26  #Demod        : 2091
% 19.64/6.26  #Tautology    : 1028
% 19.64/6.26  #SimpNegUnit  : 56
% 19.64/6.26  #BackRed      : 7
% 19.64/6.26  
% 19.64/6.26  #Partial instantiations: 0
% 19.64/6.26  #Strategies tried      : 1
% 19.64/6.26  
% 19.64/6.26  Timing (in seconds)
% 19.64/6.26  ----------------------
% 19.64/6.27  Preprocessing        : 1.56
% 19.64/6.27  Parsing              : 0.89
% 19.64/6.27  CNF conversion       : 0.13
% 19.64/6.27  Main loop            : 3.61
% 19.64/6.27  Inferencing          : 0.83
% 19.64/6.27  Reduction            : 1.71
% 19.64/6.27  Demodulation         : 1.28
% 19.64/6.27  BG Simplification    : 0.17
% 19.64/6.27  Subsumption          : 0.75
% 19.64/6.27  Abstraction          : 0.08
% 19.64/6.27  MUC search           : 0.00
% 19.64/6.27  Cooper               : 0.00
% 19.64/6.27  Total                : 5.26
% 19.64/6.27  Index Insertion      : 0.00
% 19.64/6.27  Index Deletion       : 0.00
% 19.64/6.27  Index Matching       : 0.00
% 19.64/6.27  BG Taut test         : 0.00
%------------------------------------------------------------------------------