TSTP Solution File: ALG438-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ALG438-1 : 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 : n011.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 44.78s 26.62s
% Output   : CNFRefutation 44.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   70
% Syntax   : Number of formulae    :   75 (   6 unt;  67 typ;   0 def)
%            Number of atoms       :   10 (   4 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    7 (   5   ~;   2   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   83 (  61   >;  22   *;   0   +;   0  <<)
%            Number of predicates  :   50 (  48 usr;   1 prp; 0-3 aty)
%            Number of functors    :   19 (  19 usr;   6 con; 0-3 aty)
%            Number of variables   :    8 (;   8   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_lessequals > c_HOL_Oord__class_Oless > c_Polynomial_Opos__poly > class_Ring__and__Field_Osemiring > class_Ring__and__Field_Oring__no__zero__divisors > class_Ring__and__Field_Opordered__semiring > 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__field > 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_Oidom > class_Ring__and__Field_Ofield > 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_RealVector_Oreal__normed__algebra > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > 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 > class_OrderedGroup_Omonoid__add > class_OrderedGroup_Olordered__ab__group__add > 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_Int_Onumber__ring > class_HOL_Ozero > c_Polynomial_Osynthetic__div > c_Polynomial_Osmult > c_Polynomial_Opoly > c_Polynomial_Opcompose > c_Polynomial_OpCons > c_HOL_Otimes__class_Otimes > c_HOL_Oplus__class_Oplus > c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly > c_HOL_Oinverse__class_Oinverse > #nlpp > v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xbasic__cqe__conv1__5__1 > v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xbasic__cqe__conv1__3__1 > tc_Polynomial_Opoly > c_HOL_Ozero__class_Ozero > v_q > v_p > v_b > v_a > tc_Complex_Ocomplex > t_a

%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_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(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xbasic__cqe__conv1__5__1,type,
    v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xbasic__cqe__conv1__5__1: $i > $i ).

tff(c_HOL_Oord__class_Oless,type,
    c_HOL_Oord__class_Oless: ( $i * $i * $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_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_Ring__and__Field_Ocomm__semiring,type,
    class_Ring__and__Field_Ocomm__semiring: $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(c_Polynomial_Osynthetic__div,type,
    c_Polynomial_Osynthetic__div: ( $i * $i * $i ) > $i ).

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

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(v_b,type,
    v_b: $i ).

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

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_Opordered__ring,type,
    class_Ring__and__Field_Opordered__ring: $i > $o ).

tff(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xbasic__cqe__conv1__3__1,type,
    v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xbasic__cqe__conv1__3__1: $i > $i ).

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

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

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_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_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_OrderedGroup_Opordered__cancel__ab__semigroup__add,type,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).

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

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

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(v_a,type,
    v_a: $i ).

tff(class_OrderedGroup_Omonoid__add,type,
    class_OrderedGroup_Omonoid__add: $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_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_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_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_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(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(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly,type,
    c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly: ( $i * $i * $i ) > $i ).

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

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

tff(f_2845,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
    file(unknown,unknown) ).

tff(f_2327,axiom,
    ! [T_a,V_a,V_p,V_q] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
      | ( c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_a,V_q,T_a),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a),tc_Polynomial_Opoly(T_a)) ) ),
    file(unknown,unknown) ).

tff(f_2826,axiom,
    c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_a,c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    file(unknown,unknown) ).

tff(c_684,plain,
    class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
    inference(cnfTransformation,[status(thm)],[f_2845]) ).

tff(c_496,plain,
    ! [V_a_769,V_q_771,T_a_768,V_p_770] :
      ( ( c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_a_769,V_q_771,T_a_768),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a_768),c_HOL_Otimes__class_Otimes(V_p_770,V_q_771,tc_Polynomial_Opoly(T_a_768)),T_a_768),tc_Polynomial_Opoly(T_a_768)) = c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(V_a_769,V_p_770,T_a_768),V_q_771,tc_Polynomial_Opoly(T_a_768)) )
      | ~ class_Ring__and__Field_Ocomm__semiring__0(T_a_768) ),
    inference(cnfTransformation,[status(thm)],[f_2327]) ).

tff(c_662,plain,
    c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(v_a,c_Polynomial_OpCons(v_b,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(cnfTransformation,[status(thm)],[f_2826]) ).

tff(c_161388,plain,
    ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
    inference(superposition,[status(thm),theory(equality)],[c_496,c_662]) ).

tff(c_161401,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_684,c_161388]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : ALG438-1 : 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
% 0.16/0.37  % Computer : n011.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Thu Aug  3 20:16:36 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 44.78/26.62  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 44.78/26.62  
% 44.78/26.62  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 44.78/26.65  
% 44.78/26.65  Inference rules
% 44.78/26.65  ----------------------
% 44.78/26.65  #Ref     : 52
% 44.78/26.65  #Sup     : 40057
% 44.78/26.65  #Fact    : 8
% 44.78/26.65  #Define  : 0
% 44.78/26.65  #Split   : 11
% 44.78/26.65  #Chain   : 0
% 44.78/26.65  #Close   : 0
% 44.78/26.65  
% 44.78/26.65  Ordering : KBO
% 44.78/26.65  
% 44.78/26.65  Simplification rules
% 44.78/26.65  ----------------------
% 44.78/26.65  #Subsume      : 9344
% 44.78/26.65  #Demod        : 29322
% 44.78/26.65  #Tautology    : 7558
% 44.78/26.65  #SimpNegUnit  : 0
% 44.78/26.65  #BackRed      : 2
% 44.78/26.65  
% 44.78/26.65  #Partial instantiations: 0
% 44.78/26.65  #Strategies tried      : 1
% 44.78/26.65  
% 44.78/26.65  Timing (in seconds)
% 44.78/26.65  ----------------------
% 44.78/26.65  Preprocessing        : 1.20
% 44.78/26.65  Parsing              : 0.69
% 44.78/26.65  CNF conversion       : 0.10
% 44.78/26.65  Main loop            : 24.35
% 44.78/26.65  Inferencing          : 3.80
% 44.78/26.65  Reduction            : 11.25
% 44.78/26.65  Demodulation         : 9.83
% 44.78/26.65  BG Simplification    : 0.53
% 44.78/26.65  Subsumption          : 7.57
% 44.78/26.66  Abstraction          : 0.60
% 44.78/26.66  MUC search           : 0.00
% 44.78/26.66  Cooper               : 0.00
% 44.78/26.66  Total                : 25.60
% 44.78/26.66  Index Insertion      : 0.00
% 44.78/26.66  Index Deletion       : 0.00
% 44.78/26.66  Index Matching       : 0.00
% 44.78/26.66  BG Taut test         : 0.00
%------------------------------------------------------------------------------