TSTP Solution File: ALG436-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ALG436-1 : 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 10:32:43 EDT 2023

% Result   : Unsatisfiable 11.98s 3.90s
% Output   : CNFRefutation 12.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   70
% Syntax   : Number of formulae    :   80 (   6 unt;  66 typ;   0 def)
%            Number of atoms       :   22 (   0 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   18 (  10   ~;   8   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   83 (  60   >;  23   *;   0   +;   0  <<)
%            Number of predicates  :   46 (  45 usr;   1 prp; 0-3 aty)
%            Number of functors    :   21 (  21 usr;   6 con; 0-3 aty)
%            Number of variables   :    0 (;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ 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_Oordered__field > 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_Odivision__ring > class_Ring__and__Field_Odivision__by__zero > 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__field > class_RealVector_Oreal__normed__algebra > class_RealVector_Oreal__field > 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_Divides_Osemiring__div > class_Divides_Oring__div > c_Power_Opower__class_Opower > c_Polynomial_Osmult > c_Polynomial_Opoly__gcd > c_HOL_Otimes__class_Otimes > c_HOL_Oplus__class_Oplus > c_HOL_Ominus__class_Ominus > c_HOL_Oinverse__class_Odivide > c_Divides_Odiv__class_Omod > c_Divides_Odiv__class_Odiv > c_HOL_Ouminus__class_Ouminus > c_HOL_Oinverse__class_Oinverse > c_HOL_Oabs__class_Oabs > #nlpp > tc_Polynomial_Opoly > c_HOL_Ozero__class_Ozero > c_HOL_Oone__class_Oone > v_r > v_q > v_p_H > v_p > tc_Rational_Orat > 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_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(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_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_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(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(c_HOL_Oinverse__class_Odivide,type,
    c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).

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

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_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(v_p_H,type,
    v_p_H: $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(class_Ring__and__Field_Odivision__ring,type,
    class_Ring__and__Field_Odivision__ring: $i > $o ).

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

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

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

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

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

tff(f_2535,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_r,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    file(unknown,unknown) ).

tff(f_2539,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(v_p,v_r,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    file(unknown,unknown) ).

tff(f_2547,axiom,
    ( c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | c_Ring__and__Field_Odvd__class_Odvd(v_p,v_r,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    file(unknown,unknown) ).

tff(f_2544,axiom,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_r,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    file(unknown,unknown) ).

tff(c_748,plain,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_r,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    inference(cnfTransformation,[status(thm)],[f_2535]) ).

tff(c_2844,plain,
    ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_r,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(splitLeft,[status(thm)],[c_748]) ).

tff(c_750,plain,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | c_Ring__and__Field_Odvd__class_Odvd(v_p,v_r,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    inference(cnfTransformation,[status(thm)],[f_2539]) ).

tff(c_3441,plain,
    ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(negUnitSimplification,[status(thm)],[c_2844,c_750]) ).

tff(c_754,plain,
    ( c_Ring__and__Field_Odvd__class_Odvd(v_p,v_r,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    inference(cnfTransformation,[status(thm)],[f_2547]) ).

tff(c_3865,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3441,c_2844,c_754]) ).

tff(c_3867,plain,
    c_Ring__and__Field_Odvd__class_Odvd(v_p,v_r,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(splitRight,[status(thm)],[c_748]) ).

tff(c_3866,plain,
    c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(splitRight,[status(thm)],[c_748]) ).

tff(c_752,plain,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_r,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    inference(cnfTransformation,[status(thm)],[f_2544]) ).

tff(c_4543,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_3867,c_3866,c_752]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ALG436-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14  % 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
% 0.13/0.35  % Computer : n021.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 20:19:21 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 11.98/3.90  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.98/3.90  
% 11.98/3.90  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.27/3.93  
% 12.27/3.93  Inference rules
% 12.27/3.93  ----------------------
% 12.27/3.93  #Ref     : 4
% 12.27/3.93  #Sup     : 725
% 12.27/3.93  #Fact    : 0
% 12.27/3.93  #Define  : 0
% 12.27/3.93  #Split   : 1
% 12.27/3.93  #Chain   : 0
% 12.27/3.93  #Close   : 0
% 12.27/3.93  
% 12.27/3.93  Ordering : KBO
% 12.27/3.93  
% 12.27/3.93  Simplification rules
% 12.27/3.93  ----------------------
% 12.27/3.93  #Subsume      : 115
% 12.27/3.93  #Demod        : 364
% 12.27/3.93  #Tautology    : 545
% 12.27/3.93  #SimpNegUnit  : 2
% 12.27/3.93  #BackRed      : 0
% 12.27/3.93  
% 12.27/3.93  #Partial instantiations: 0
% 12.27/3.93  #Strategies tried      : 1
% 12.27/3.93  
% 12.27/3.93  Timing (in seconds)
% 12.27/3.93  ----------------------
% 12.27/3.93  Preprocessing        : 1.29
% 12.27/3.93  Parsing              : 0.70
% 12.27/3.93  CNF conversion       : 0.11
% 12.27/3.93  Main loop            : 1.50
% 12.27/3.93  Inferencing          : 0.38
% 12.27/3.93  Reduction            : 0.59
% 12.27/3.93  Demodulation         : 0.40
% 12.27/3.93  BG Simplification    : 0.13
% 12.27/3.93  Subsumption          : 0.31
% 12.27/3.93  Abstraction          : 0.04
% 12.27/3.94  MUC search           : 0.00
% 12.27/3.94  Cooper               : 0.00
% 12.27/3.94  Total                : 2.84
% 12.27/3.94  Index Insertion      : 0.00
% 12.27/3.94  Index Deletion       : 0.00
% 12.27/3.94  Index Matching       : 0.00
% 12.27/3.94  BG Taut test         : 0.00
%------------------------------------------------------------------------------