TSTP Solution File: ALG369-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ALG369-1 : 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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/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 10:32:37 EDT 2023

% Result   : Unsatisfiable 25.59s 10.84s
% Output   : CNFRefutation 25.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   82
% Syntax   : Number of formulae    :   90 (   9 unt;  77 typ;   0 def)
%            Number of atoms       :   22 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   22 (  13   ~;   9   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   90 (  73   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :   62 (  61 usr;   2 prp; 0-3 aty)
%            Number of functors    :   16 (  16 usr;   3 con; 0-3 aty)
%            Number of variables   :    3 (;   3   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_lessequals > c_HOL_Oord__class_Oless > class_SEQ_Obanach > class_Ring__and__Field_Ozero__neq__one > class_Ring__and__Field_Osgn__if > 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__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__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_Olordered__ring > 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 > class_Ring__and__Field_Oabs__if > 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_RealVector_Oreal__field > class_RealVector_Oreal__div__algebra > class_RealVector_Oreal__algebra__1 > 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__abs > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Omonoid__mult > class_OrderedGroup_Omonoid__add > class_OrderedGroup_Olordered__ab__group__add__abs > class_OrderedGroup_Olordered__ab__group__add > class_OrderedGroup_Ocomm__monoid__mult > class_OrderedGroup_Ocomm__monoid__add > class_OrderedGroup_Ocancel__semigroup__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 > c_HOL_Otimes__class_Otimes > c_HOL_Oplus__class_Oplus > c_HOL_Oinverse__class_Odivide > v_sko__CHAINED__1 > c_Transcendental_Oexp > c_RealVector_Oof__real > c_RealVector_Onorm__class_Onorm > c_HOL_Osgn__class_Osgn > c_HOL_Oinverse__class_Oinverse > c_HOL_Oabs__class_Oabs > #nlpp > c_Transcendental_Oln > c_HOL_Ozero__class_Ozero > c_HOL_Oone__class_Oone > v_thesis____ > v_m____ > v_e > tc_RealDef_Oreal

%Foreground sorts:

%Background operators:

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

tff(c_Transcendental_Oln,type,
    c_Transcendental_Oln: $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(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(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_RealVector_Oreal__normed__algebra__1,type,
    class_RealVector_Oreal__normed__algebra__1: $i > $o ).

tff(class_Ring__and__Field_Ocomm__semiring,type,
    class_Ring__and__Field_Ocomm__semiring: $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_OrderedGroup_Oab__semigroup__add,type,
    class_OrderedGroup_Oab__semigroup__add: $i > $o ).

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

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

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

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

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_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(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_Opordered__cancel__ab__semigroup__add,type,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $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(v_m____,type,
    v_m____: $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(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(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_RealVector_Oreal__algebra__1,type,
    class_RealVector_Oreal__algebra__1: $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(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_Transcendental_Oexp,type,
    c_Transcendental_Oexp: ( $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

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

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

tff(f_5184,axiom,
    c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),
    file(unknown,unknown) ).

tff(f_5185,axiom,
    c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
    file(unknown,unknown) ).

tff(f_5186,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_e,v_m____),tc_RealDef_Oreal),
    file(unknown,unknown) ).

tff(f_5188,axiom,
    ~ v_thesis____,
    file(unknown,unknown) ).

tff(f_4735,axiom,
    ! [V_d] :
      ( v_thesis____
      | ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(V_d,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d,tc_RealDef_Oreal) ),
    file(unknown,unknown) ).

tff(c_1132,plain,
    c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_5184]) ).

tff(c_1134,plain,
    c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_5185]) ).

tff(c_1136,plain,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__CHAINED__1(v_e,v_m____),tc_RealDef_Oreal),
    inference(cnfTransformation,[status(thm)],[f_5186]) ).

tff(c_1138,plain,
    ~ v_thesis____,
    inference(cnfTransformation,[status(thm)],[f_5188]) ).

tff(c_1030,plain,
    ! [V_d_1491] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d_1491,tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(V_d_1491,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(V_d_1491,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)
      | v_thesis____ ),
    inference(cnfTransformation,[status(thm)],[f_4735]) ).

tff(c_53161,plain,
    ! [V_d_2376] :
      ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d_2376,tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(V_d_2376,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
      | ~ c_HOL_Oord__class_Oless(V_d_2376,c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(negUnitSimplification,[status(thm)],[c_1138,c_1030]) ).

tff(c_53282,plain,
    ( ~ c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(v_sko__CHAINED__1(v_e,v_m____),c_HOL_Oinverse__class_Odivide(v_e,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    inference(resolution,[status(thm)],[c_1136,c_53161]) ).

tff(c_53373,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1132,c_1134,c_53282]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : ALG369-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.15  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.37  % Computer : n011.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit : 300
% 0.14/0.37  % WCLimit  : 300
% 0.14/0.37  % DateTime : Thu Aug  3 20:23:06 EDT 2023
% 0.14/0.37  % CPUTime  : 
% 25.59/10.84  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.59/10.85  
% 25.59/10.85  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 25.59/10.88  
% 25.59/10.88  Inference rules
% 25.59/10.88  ----------------------
% 25.59/10.88  #Ref     : 10
% 25.59/10.88  #Sup     : 11281
% 25.59/10.88  #Fact    : 6
% 25.59/10.88  #Define  : 0
% 25.59/10.88  #Split   : 4
% 25.59/10.88  #Chain   : 0
% 25.59/10.88  #Close   : 0
% 25.59/10.88  
% 25.59/10.88  Ordering : KBO
% 25.59/10.88  
% 25.59/10.88  Simplification rules
% 25.59/10.88  ----------------------
% 25.59/10.88  #Subsume      : 2481
% 25.59/10.88  #Demod        : 7411
% 25.59/10.88  #Tautology    : 3392
% 25.59/10.88  #SimpNegUnit  : 505
% 25.59/10.88  #BackRed      : 5
% 25.59/10.88  
% 25.59/10.88  #Partial instantiations: 0
% 25.59/10.88  #Strategies tried      : 1
% 25.59/10.88  
% 25.59/10.88  Timing (in seconds)
% 25.59/10.88  ----------------------
% 25.59/10.88  Preprocessing        : 1.54
% 25.59/10.88  Parsing              : 0.90
% 25.59/10.88  CNF conversion       : 0.12
% 25.59/10.88  Main loop            : 8.12
% 25.59/10.88  Inferencing          : 1.47
% 25.59/10.88  Reduction            : 3.84
% 25.59/10.88  Demodulation         : 2.89
% 25.59/10.88  BG Simplification    : 0.23
% 25.59/10.88  Subsumption          : 2.17
% 25.59/10.88  Abstraction          : 0.15
% 25.59/10.88  MUC search           : 0.00
% 25.59/10.88  Cooper               : 0.00
% 25.59/10.88  Total                : 9.71
% 25.59/10.88  Index Insertion      : 0.00
% 25.59/10.88  Index Deletion       : 0.00
% 25.59/10.88  Index Matching       : 0.00
% 25.59/10.88  BG Taut test         : 0.00
%------------------------------------------------------------------------------