TSTP Solution File: SWV629-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWV629-1 : 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 : 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 11:05:21 EDT 2023

% Result   : Unsatisfiable 8.74s 3.12s
% Output   : CNFRefutation 8.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   55
% Syntax   : Number of formulae    :   62 (   8 unt;  51 typ;   0 def)
%            Number of atoms       :   14 (   8 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    8 (   5   ~;   3   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   69 (  48   >;  21   *;   0   +;   0  <<)
%            Number of predicates  :   35 (  33 usr;   1 prp; 0-3 aty)
%            Number of functors    :   18 (  18 usr;   3 con; 0-3 aty)
%            Number of variables   :    6 (;   6   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_Ring__and__Field_Odvd__class_Odvd > c_Parity_Oeven__odd__class_Oeven > c_Int_Oiszero > class_Ring__and__Field_Ozero__neq__one > class_Ring__and__Field_Osgn__if > class_Ring__and__Field_Osemiring__1 > class_Ring__and__Field_Osemiring__0 > class_Ring__and__Field_Oring__no__zero__divisors > class_Ring__and__Field_Oring__1__no__zero__divisors > 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_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_OrderedGroup_Opordered__ab__group__add__abs > class_OrderedGroup_Omonoid__mult > class_OrderedGroup_Ocomm__monoid__mult > class_OrderedGroup_Oab__semigroup__mult > class_OrderedGroup_Oab__semigroup__idem__mult > class_Nat_Osemiring__char__0 > class_Int_Onumber__ring > class_Divides_Osemiring__div > c_Power_Opower__class_Opower > c_HOL_Otimes__class_Otimes > c_HOL_Oinverse__class_Odivide > c_GCD_Ogcd__class_Olcm > c_GCD_Ogcd__class_Ogcd > c_Divides_Odiv__class_Odiv > c_Nat_Osemiring__1__class_Oof__nat > c_HOL_Osgn__class_Osgn > c_HOL_Oinverse__class_Oinverse > c_HOL_Oabs__class_Oabs > c_Fact_Ofact__class_Ofact > #nlpp > c_HOL_Ozero__class_Ozero > c_HOL_Oone__class_Oone > c_FFT__Mirabelle_Oroot > c_Complex_Ocnj > tc_nat > tc_Complex_Ocomplex > c_Complex_Oii

%Foreground sorts:

%Background operators:

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

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

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

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

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

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_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_Nat_Osemiring__1__class_Oof__nat,type,
    c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).

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

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

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(c_Complex_Oii,type,
    c_Complex_Oii: $i ).

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

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(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_Ocomm__monoid__mult,type,
    class_OrderedGroup_Ocomm__monoid__mult: $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_RealVector_Oreal__normed__vector,type,
    class_RealVector_Oreal__normed__vector: $i > $o ).

tff(class_Nat_Osemiring__char__0,type,
    class_Nat_Osemiring__char__0: $i > $o ).

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(c_HOL_Osgn__class_Osgn,type,
    c_HOL_Osgn__class_Osgn: ( $i * $i ) > $i ).

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

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

tff(class_Ring__and__Field_Odvd,type,
    class_Ring__and__Field_Odvd: $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(c_Complex_Ocnj,type,
    c_Complex_Ocnj: $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(c_Int_Oiszero,type,
    c_Int_Oiszero: ( $i * $i ) > $o ).

tff(class_Ring__and__Field_Osemiring__1,type,
    class_Ring__and__Field_Osemiring__1: $i > $o ).

tff(f_2075,axiom,
    c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
    file(unknown,unknown) ).

tff(f_2095,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
    file(unknown,unknown) ).

tff(f_1923,axiom,
    ! [T_a,V_x] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
      | ( c_Power_Opower__class_Opower(V_x,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_x ) ),
    file(unknown,unknown) ).

tff(f_1999,axiom,
    ! [V_n] : ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
    file(unknown,unknown) ).

tff(c_704,plain,
    c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
    inference(cnfTransformation,[status(thm)],[f_2075]) ).

tff(c_744,plain,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
    inference(cnfTransformation,[status(thm)],[f_2095]) ).

tff(c_1492,plain,
    ! [V_x_893,T_a_894] :
      ( ( c_Power_Opower__class_Opower(V_x_893,c_HOL_Oone__class_Oone(tc_nat),T_a_894) = V_x_893 )
      | ~ class_Ring__and__Field_Ocomm__semiring__1(T_a_894) ),
    inference(cnfTransformation,[status(thm)],[f_1923]) ).

tff(c_668,plain,
    ! [V_n_812] : ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n_812),V_n_812,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
    inference(cnfTransformation,[status(thm)],[f_1999]) ).

tff(c_1499,plain,
    ( ( c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) )
    | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
    inference(superposition,[status(thm),theory(equality)],[c_1492,c_668]) ).

tff(c_1509,plain,
    c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
    inference(demodulation,[status(thm),theory(equality)],[c_744,c_1499]) ).

tff(c_1511,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_704,c_1509]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : SWV629-1 : TPTP v8.1.2. Released v4.1.0.
% 0.08/0.15  % 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 : n031.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 23:28:00 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 8.74/3.12  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.74/3.12  
% 8.74/3.12  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.89/3.16  
% 8.89/3.16  Inference rules
% 8.89/3.16  ----------------------
% 8.89/3.16  #Ref     : 4
% 8.89/3.16  #Sup     : 162
% 8.89/3.16  #Fact    : 0
% 8.89/3.16  #Define  : 0
% 8.89/3.16  #Split   : 0
% 8.89/3.16  #Chain   : 0
% 8.89/3.16  #Close   : 0
% 8.89/3.16  
% 8.89/3.16  Ordering : KBO
% 8.89/3.16  
% 8.89/3.16  Simplification rules
% 8.89/3.16  ----------------------
% 8.89/3.16  #Subsume      : 86
% 8.89/3.16  #Demod        : 76
% 8.89/3.16  #Tautology    : 173
% 8.89/3.16  #SimpNegUnit  : 3
% 8.89/3.16  #BackRed      : 0
% 8.89/3.16  
% 8.89/3.16  #Partial instantiations: 0
% 8.89/3.16  #Strategies tried      : 1
% 8.89/3.16  
% 8.89/3.16  Timing (in seconds)
% 8.89/3.16  ----------------------
% 8.89/3.16  Preprocessing        : 1.23
% 8.89/3.16  Parsing              : 0.66
% 8.89/3.16  CNF conversion       : 0.10
% 8.89/3.16  Main loop            : 0.76
% 8.89/3.16  Inferencing          : 0.17
% 8.89/3.16  Reduction            : 0.32
% 8.89/3.16  Demodulation         : 0.22
% 8.89/3.16  BG Simplification    : 0.10
% 8.89/3.17  Subsumption          : 0.16
% 8.89/3.17  Abstraction          : 0.03
% 8.89/3.17  MUC search           : 0.00
% 8.89/3.17  Cooper               : 0.00
% 8.89/3.17  Total                : 2.05
% 8.89/3.17  Index Insertion      : 0.00
% 8.89/3.17  Index Deletion       : 0.00
% 8.89/3.17  Index Matching       : 0.00
% 8.89/3.17  BG Taut test         : 0.00
%------------------------------------------------------------------------------