TSTP Solution File: ALG434-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ALG434-1 : 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 : n002.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 10:32:43 EDT 2023

% Result   : Unsatisfiable 18.79s 6.25s
% Output   : CNFRefutation 18.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   65
% Syntax   : Number of formulae    :   71 (   7 unt;  61 typ;   0 def)
%            Number of atoms       :   15 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   13 (   8   ~;   5   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   85 (  57   >;  28   *;   0   +;   0  <<)
%            Number of predicates  :   43 (  42 usr;   1 prp; 0-5 aty)
%            Number of functors    :   19 (  19 usr;   4 con; 0-3 aty)
%            Number of variables   :    8 (;   8   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_Polynomial_Opdivmod__rel > c_Ring__and__Field_Odvd__class_Odvd > 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_Oordered__ring__strict > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Ono__zero__divisors > class_Ring__and__Field_Omult__zero > class_Ring__and__Field_Oidom > class_Ring__and__Field_Ofield > class_Ring__and__Field_Odvd > 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_RealVector_Oreal__normed__algebra > class_Power_Opower > class_OrderedGroup_Opordered__ab__group__add__abs > class_OrderedGroup_Oordered__ab__group__add > class_OrderedGroup_Omonoid__mult > class_OrderedGroup_Omonoid__add > 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_Oboolean__algebra > class_Int_Onumber__ring > class_HOL_Ozero > class_Divides_Osemiring__div > class_Divides_Oring__div > c_Power_Opower__class_Opower > c_Polynomial_Osmult > c_Polynomial_Opoly__gcd > c_Polynomial_Opoly > c_Polynomial_OpCons > c_HOL_Otimes__class_Otimes > c_HOL_Oplus__class_Oplus > c_HOL_Ominus__class_Ominus > c_Divides_Odiv__class_Omod > c_Divides_Odiv__class_Odiv > c_HOL_Ouminus__class_Ouminus > c_HOL_Oabs__class_Oabs > #nlpp > tc_Polynomial_Opoly > c_HOL_Ozero__class_Ozero > c_HOL_Oone__class_Oone > v_q > v_p > v_a > tc_Complex_Ocomplex

%Foreground sorts:

%Background operators:

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

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_Int_Onumber__ring,type,
    class_Int_Onumber__ring: $i > $o ).

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

tff(class_Ring__and__Field_Osemiring,type,
    class_Ring__and__Field_Osemiring: $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(class_Ring__and__Field_Oring,type,
    class_Ring__and__Field_Oring: $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(v_q,type,
    v_q: $i ).

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_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_Ozero__neq__one,type,
    class_Ring__and__Field_Ozero__neq__one: $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(class_Ring__and__Field_Ocomm__ring__1,type,
    class_Ring__and__Field_Ocomm__ring__1: $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_Divides_Oring__div,type,
    class_Divides_Oring__div: $i > $o ).

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

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

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

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

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

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

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(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_Ring__and__Field_Odvd__class_Odvd,type,
    c_Ring__and__Field_Odvd__class_Odvd: ( $i * $i * $i ) > $o ).

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

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

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

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

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

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

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

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

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

tff(f_2429,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
    file(unknown,unknown) ).

tff(f_2415,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    file(unknown,unknown) ).

tff(f_2389,axiom,
    ! [T_a,V_p,V_a,V_q] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | c_Ring__and__Field_Odvd__class_Odvd(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a))
      | ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a)) ),
    file(unknown,unknown) ).

tff(f_2417,axiom,
    ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    file(unknown,unknown) ).

tff(c_766,plain,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
    inference(cnfTransformation,[status(thm)],[f_2429]) ).

tff(c_748,plain,
    c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(cnfTransformation,[status(thm)],[f_2415]) ).

tff(c_35763,plain,
    ! [V_p_1973,V_q_1974,T_a_1975,V_a_1976] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(V_p_1973,V_q_1974,tc_Polynomial_Opoly(T_a_1975))
      | c_Ring__and__Field_Odvd__class_Odvd(V_p_1973,c_Polynomial_Osmult(V_a_1976,V_q_1974,T_a_1975),tc_Polynomial_Opoly(T_a_1975))
      | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a_1975) ),
    inference(cnfTransformation,[status(thm)],[f_2389]) ).

tff(c_750,plain,
    ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(cnfTransformation,[status(thm)],[f_2417]) ).

tff(c_35795,plain,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
    inference(resolution,[status(thm)],[c_35763,c_750]) ).

tff(c_35822,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_766,c_748,c_35795]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : ALG434-1 : 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
% 0.15/0.37  % Computer : n002.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Thu Aug  3 20:31:01 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 18.79/6.25  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.79/6.26  
% 18.79/6.26  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.79/6.28  
% 18.79/6.28  Inference rules
% 18.79/6.28  ----------------------
% 18.79/6.28  #Ref     : 22
% 18.79/6.28  #Sup     : 7704
% 18.79/6.28  #Fact    : 0
% 18.79/6.28  #Define  : 0
% 18.79/6.28  #Split   : 4
% 18.79/6.28  #Chain   : 0
% 18.79/6.28  #Close   : 0
% 18.79/6.28  
% 18.79/6.28  Ordering : KBO
% 18.79/6.28  
% 18.79/6.28  Simplification rules
% 18.79/6.28  ----------------------
% 18.79/6.28  #Subsume      : 1532
% 18.79/6.28  #Demod        : 6212
% 18.79/6.28  #Tautology    : 3570
% 18.79/6.28  #SimpNegUnit  : 32
% 18.79/6.28  #BackRed      : 6
% 18.79/6.28  
% 18.79/6.28  #Partial instantiations: 0
% 18.79/6.28  #Strategies tried      : 1
% 18.79/6.28  
% 18.79/6.28  Timing (in seconds)
% 18.79/6.28  ----------------------
% 18.79/6.29  Preprocessing        : 1.31
% 18.79/6.29  Parsing              : 0.72
% 18.79/6.29  CNF conversion       : 0.11
% 18.79/6.29  Main loop            : 3.84
% 18.79/6.29  Inferencing          : 0.95
% 18.79/6.29  Reduction            : 1.53
% 18.79/6.29  Demodulation         : 1.14
% 18.79/6.29  BG Simplification    : 0.17
% 18.79/6.29  Subsumption          : 0.99
% 18.79/6.29  Abstraction          : 0.11
% 18.79/6.29  MUC search           : 0.00
% 18.79/6.29  Cooper               : 0.00
% 18.79/6.29  Total                : 5.20
% 18.79/6.29  Index Insertion      : 0.00
% 18.79/6.29  Index Deletion       : 0.00
% 18.79/6.29  Index Matching       : 0.00
% 18.79/6.29  BG Taut test         : 0.00
%------------------------------------------------------------------------------