TSTP Solution File: SET803+4 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET803+4 : TPTP v8.1.2. Released v3.2.0.
% 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 : n013.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 10:57:02 EDT 2023

% Result   : Theorem 4.83s 2.20s
% Output   : CNFRefutation 5.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   36
% Syntax   : Number of formulae    :   61 (  15 unt;  33 typ;   0 def)
%            Number of atoms       :   54 (   8 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   50 (  24   ~;  15   |;   5   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   77 (  28   >;  49   *;   0   +;   0  <<)
%            Number of predicates  :   14 (  12 usr;   1 prp; 0-4 aty)
%            Number of functors    :   21 (  21 usr;   5 con; 0-4 aty)
%            Number of variables   :   35 (;  34   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ least_upper_bound > greatest_lower_bound > upper_bound > min > max > lower_bound > least > greatest > apply > total_order > order > member > #nlpp > #skF_13 > #skF_6 > #skF_20 > #skF_18 > #skF_17 > #skF_12 > #skF_19 > #skF_3 > #skF_15 > #skF_16 > #skF_8 > #skF_21 > #skF_11 > #skF_9 > #skF_14 > #skF_2 > #skF_7 > #skF_1 > #skF_5 > #skF_4 > #skF_10

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_13',type,
    '#skF_13': ( $i * $i * $i ) > $i ).

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

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

tff('#skF_6',type,
    '#skF_6': ( $i * $i ) > $i ).

tff('#skF_20',type,
    '#skF_20': $i ).

tff('#skF_18',type,
    '#skF_18': $i ).

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

tff('#skF_17',type,
    '#skF_17': $i ).

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

tff('#skF_12',type,
    '#skF_12': ( $i * $i * $i ) > $i ).

tff('#skF_19',type,
    '#skF_19': $i ).

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

tff('#skF_3',type,
    '#skF_3': ( $i * $i ) > $i ).

tff('#skF_15',type,
    '#skF_15': ( $i * $i * $i * $i ) > $i ).

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

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

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

tff('#skF_16',type,
    '#skF_16': ( $i * $i * $i * $i ) > $i ).

tff('#skF_8',type,
    '#skF_8': ( $i * $i ) > $i ).

tff('#skF_21',type,
    '#skF_21': $i ).

tff('#skF_11',type,
    '#skF_11': ( $i * $i * $i ) > $i ).

tff('#skF_9',type,
    '#skF_9': ( $i * $i * $i ) > $i ).

tff('#skF_14',type,
    '#skF_14': ( $i * $i * $i ) > $i ).

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

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

tff('#skF_2',type,
    '#skF_2': ( $i * $i ) > $i ).

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

tff('#skF_7',type,
    '#skF_7': ( $i * $i ) > $i ).

tff('#skF_1',type,
    '#skF_1': ( $i * $i ) > $i ).

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

tff('#skF_5',type,
    '#skF_5': ( $i * $i ) > $i ).

tff('#skF_4',type,
    '#skF_4': ( $i * $i ) > $i ).

tff('#skF_10',type,
    '#skF_10': ( $i * $i * $i ) > $i ).

tff(f_190,negated_conjecture,
    ~ ! [R,E] :
        ( order(R,E)
       => ! [M1,M2] :
            ( ( max(M1,R,E)
              & max(M2,R,E)
              & ( M1 != M2 ) )
           => ~ ? [M] : greatest(M,R,E) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV15) ).

tff(f_116,axiom,
    ! [R,E,M] :
      ( greatest(M,R,E)
    <=> ( member(M,E)
        & ! [X] :
            ( member(X,E)
           => apply(R,X,M) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',greatest) ).

tff(f_136,axiom,
    ! [R,E,M] :
      ( max(M,R,E)
    <=> ( member(M,E)
        & ! [X] :
            ( ( member(X,E)
              & apply(R,M,X) )
           => ( M = X ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',max) ).

tff(c_212,plain,
    greatest('#skF_21','#skF_17','#skF_18'),
    inference(cnfTransformation,[status(thm)],[f_190]) ).

tff(c_232,plain,
    ! [M_92,E_93,R_94] :
      ( member(M_92,E_93)
      | ~ greatest(M_92,R_94,E_93) ),
    inference(cnfTransformation,[status(thm)],[f_116]) ).

tff(c_236,plain,
    member('#skF_21','#skF_18'),
    inference(resolution,[status(thm)],[c_212,c_232]) ).

tff(c_218,plain,
    max('#skF_19','#skF_17','#skF_18'),
    inference(cnfTransformation,[status(thm)],[f_190]) ).

tff(c_216,plain,
    max('#skF_20','#skF_17','#skF_18'),
    inference(cnfTransformation,[status(thm)],[f_190]) ).

tff(c_223,plain,
    ! [M_89,E_90,R_91] :
      ( member(M_89,E_90)
      | ~ max(M_89,R_91,E_90) ),
    inference(cnfTransformation,[status(thm)],[f_136]) ).

tff(c_230,plain,
    member('#skF_20','#skF_18'),
    inference(resolution,[status(thm)],[c_216,c_223]) ).

tff(c_263,plain,
    ! [R_126,X_127,M_128,E_129] :
      ( apply(R_126,X_127,M_128)
      | ~ member(X_127,E_129)
      | ~ greatest(M_128,R_126,E_129) ),
    inference(cnfTransformation,[status(thm)],[f_116]) ).

tff(c_305,plain,
    ! [R_138,M_139] :
      ( apply(R_138,'#skF_20',M_139)
      | ~ greatest(M_139,R_138,'#skF_18') ),
    inference(resolution,[status(thm)],[c_230,c_263]) ).

tff(c_309,plain,
    apply('#skF_17','#skF_20','#skF_21'),
    inference(resolution,[status(thm)],[c_212,c_305]) ).

tff(c_411,plain,
    ! [X_185,M_186,R_187,E_188] :
      ( ( X_185 = M_186 )
      | ~ apply(R_187,M_186,X_185)
      | ~ member(X_185,E_188)
      | ~ max(M_186,R_187,E_188) ),
    inference(cnfTransformation,[status(thm)],[f_136]) ).

tff(c_424,plain,
    ! [E_188] :
      ( ( '#skF_20' = '#skF_21' )
      | ~ member('#skF_21',E_188)
      | ~ max('#skF_20','#skF_17',E_188) ),
    inference(resolution,[status(thm)],[c_309,c_411]) ).

tff(c_435,plain,
    ! [E_189] :
      ( ~ member('#skF_21',E_189)
      | ~ max('#skF_20','#skF_17',E_189) ),
    inference(splitLeft,[status(thm)],[c_424]) ).

tff(c_442,plain,
    ~ member('#skF_21','#skF_18'),
    inference(resolution,[status(thm)],[c_216,c_435]) ).

tff(c_447,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_236,c_442]) ).

tff(c_448,plain,
    '#skF_20' = '#skF_21',
    inference(splitRight,[status(thm)],[c_424]) ).

tff(c_214,plain,
    '#skF_20' != '#skF_19',
    inference(cnfTransformation,[status(thm)],[f_190]) ).

tff(c_457,plain,
    '#skF_19' != '#skF_21',
    inference(demodulation,[status(thm),theory(equality)],[c_448,c_214]) ).

tff(c_231,plain,
    member('#skF_19','#skF_18'),
    inference(resolution,[status(thm)],[c_218,c_223]) ).

tff(c_300,plain,
    ! [R_136,M_137] :
      ( apply(R_136,'#skF_19',M_137)
      | ~ greatest(M_137,R_136,'#skF_18') ),
    inference(resolution,[status(thm)],[c_231,c_263]) ).

tff(c_304,plain,
    apply('#skF_17','#skF_19','#skF_21'),
    inference(resolution,[status(thm)],[c_212,c_300]) ).

tff(c_425,plain,
    ! [E_188] :
      ( ( '#skF_19' = '#skF_21' )
      | ~ member('#skF_21',E_188)
      | ~ max('#skF_19','#skF_17',E_188) ),
    inference(resolution,[status(thm)],[c_304,c_411]) ).

tff(c_494,plain,
    ! [E_195] :
      ( ~ member('#skF_21',E_195)
      | ~ max('#skF_19','#skF_17',E_195) ),
    inference(negUnitSimplification,[status(thm)],[c_457,c_425]) ).

tff(c_501,plain,
    ~ member('#skF_21','#skF_18'),
    inference(resolution,[status(thm)],[c_218,c_494]) ).

tff(c_506,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_236,c_501]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET803+4 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.14  % 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
% 0.13/0.35  % Computer : n013.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 16:50:03 EDT 2023
% 0.13/0.36  % CPUTime  : 
% 4.83/2.20  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.83/2.21  
% 4.83/2.21  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.20/2.24  
% 5.20/2.24  Inference rules
% 5.20/2.24  ----------------------
% 5.50/2.24  #Ref     : 0
% 5.50/2.24  #Sup     : 66
% 5.50/2.24  #Fact    : 0
% 5.50/2.24  #Define  : 0
% 5.50/2.24  #Split   : 1
% 5.50/2.24  #Chain   : 0
% 5.50/2.24  #Close   : 0
% 5.50/2.24  
% 5.50/2.24  Ordering : KBO
% 5.50/2.24  
% 5.50/2.24  Simplification rules
% 5.50/2.24  ----------------------
% 5.50/2.24  #Subsume      : 5
% 5.50/2.24  #Demod        : 15
% 5.50/2.24  #Tautology    : 14
% 5.50/2.24  #SimpNegUnit  : 2
% 5.50/2.24  #BackRed      : 9
% 5.50/2.24  
% 5.50/2.24  #Partial instantiations: 0
% 5.50/2.24  #Strategies tried      : 1
% 5.50/2.24  
% 5.50/2.24  Timing (in seconds)
% 5.50/2.24  ----------------------
% 5.50/2.25  Preprocessing        : 0.67
% 5.50/2.25  Parsing              : 0.29
% 5.50/2.25  CNF conversion       : 0.08
% 5.50/2.25  Main loop            : 0.47
% 5.50/2.25  Inferencing          : 0.16
% 5.50/2.25  Reduction            : 0.13
% 5.50/2.25  Demodulation         : 0.09
% 5.50/2.25  BG Simplification    : 0.06
% 5.50/2.25  Subsumption          : 0.11
% 5.50/2.25  Abstraction          : 0.02
% 5.50/2.25  MUC search           : 0.00
% 5.50/2.25  Cooper               : 0.00
% 5.50/2.25  Total                : 1.20
% 5.50/2.25  Index Insertion      : 0.00
% 5.50/2.25  Index Deletion       : 0.00
% 5.50/2.25  Index Matching       : 0.00
% 5.50/2.25  BG Taut test         : 0.00
%------------------------------------------------------------------------------