TSTP Solution File: HEN006-6 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : HEN006-6 : TPTP v8.1.2. Released v1.0.0.
% 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 : n005.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 10:42:15 EDT 2023

% Result   : Unsatisfiable 5.99s 2.54s
% Output   : CNFRefutation 6.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   63 (  36 unt;   7 typ;   0 def)
%            Number of atoms       :   80 (  39 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   52 (  28   ~;  24   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   2   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   72 (;  72   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ less_equal > divide > #nlpp > zero > identity > d > b > a

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

tff(f_53,axiom,
    ! [X,Y] :
      ( ( divide(X,Y) != zero )
      | less_equal(X,Y) ),
    file(unknown,unknown) ).

tff(f_86,axiom,
    ~ less_equal(divide(a,d),b),
    file(unknown,unknown) ).

tff(f_81,axiom,
    ! [X] : ( divide(zero,X) = zero ),
    file(unknown,unknown) ).

tff(f_83,axiom,
    ! [X] : ( divide(X,X) = zero ),
    file(unknown,unknown) ).

tff(f_59,axiom,
    ! [X,Z,Y] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
    file(unknown,unknown) ).

tff(f_71,axiom,
    ! [X,Y] :
      ( ~ less_equal(X,Y)
      | ~ less_equal(Y,X)
      | ( X = Y ) ),
    file(unknown,unknown) ).

tff(f_56,axiom,
    ! [X,Y] : less_equal(divide(X,Y),X),
    file(unknown,unknown) ).

tff(f_62,axiom,
    ! [X] : less_equal(zero,X),
    file(unknown,unknown) ).

tff(f_84,axiom,
    less_equal(divide(a,b),d),
    file(unknown,unknown) ).

tff(f_48,axiom,
    ! [X,Y] :
      ( ~ less_equal(X,Y)
      | ( divide(X,Y) = zero ) ),
    file(unknown,unknown) ).

tff(c_104,plain,
    ! [X_26,Y_27] :
      ( less_equal(X_26,Y_27)
      | ( divide(X_26,Y_27) != zero ) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_24,plain,
    ~ less_equal(divide(a,d),b),
    inference(cnfTransformation,[status(thm)],[f_86]) ).

tff(c_112,plain,
    divide(divide(a,d),b) != zero,
    inference(resolution,[status(thm)],[c_104,c_24]) ).

tff(c_18,plain,
    ! [X_15] : ( divide(zero,X_15) = zero ),
    inference(cnfTransformation,[status(thm)],[f_81]) ).

tff(c_20,plain,
    ! [X_16] : ( divide(X_16,X_16) = zero ),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_198,plain,
    ! [X_33,Z_34,Y_35] : less_equal(divide(divide(X_33,Z_34),divide(Y_35,Z_34)),divide(divide(X_33,Y_35),Z_34)),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_671,plain,
    ! [X_51,X_52] : less_equal(divide(divide(X_51,X_52),zero),divide(divide(X_51,zero),X_52)),
    inference(superposition,[status(thm),theory(equality)],[c_18,c_198]) ).

tff(c_749,plain,
    ! [X_53] : less_equal(divide(divide(X_53,divide(X_53,zero)),zero),zero),
    inference(superposition,[status(thm),theory(equality)],[c_20,c_671]) ).

tff(c_4,plain,
    ! [X_3,Y_4] :
      ( less_equal(X_3,Y_4)
      | ( divide(X_3,Y_4) != zero ) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_164,plain,
    ! [Y_30,X_31] :
      ( ( Y_30 = X_31 )
      | ~ less_equal(Y_30,X_31)
      | ~ less_equal(X_31,Y_30) ),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_175,plain,
    ! [Y_4,X_3] :
      ( ( Y_4 = X_3 )
      | ~ less_equal(Y_4,X_3)
      | ( divide(X_3,Y_4) != zero ) ),
    inference(resolution,[status(thm)],[c_4,c_164]) ).

tff(c_752,plain,
    ! [X_53] :
      ( ( divide(divide(X_53,divide(X_53,zero)),zero) = zero )
      | ( divide(zero,divide(divide(X_53,divide(X_53,zero)),zero)) != zero ) ),
    inference(resolution,[status(thm)],[c_749,c_175]) ).

tff(c_781,plain,
    ! [X_53] : ( divide(divide(X_53,divide(X_53,zero)),zero) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_18,c_752]) ).

tff(c_794,plain,
    ! [X_54] : ( divide(divide(X_54,divide(X_54,zero)),zero) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_18,c_752]) ).

tff(c_6,plain,
    ! [X_5,Y_6] : less_equal(divide(X_5,Y_6),X_5),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_509,plain,
    ! [X_45,Y_46] :
      ( ( divide(X_45,Y_46) = X_45 )
      | ~ less_equal(X_45,divide(X_45,Y_46)) ),
    inference(resolution,[status(thm)],[c_6,c_164]) ).

tff(c_539,plain,
    ! [X_3,Y_46] :
      ( ( divide(X_3,Y_46) = X_3 )
      | ( divide(X_3,divide(X_3,Y_46)) != zero ) ),
    inference(resolution,[status(thm)],[c_4,c_509]) ).

tff(c_811,plain,
    ! [X_54] :
      ( ( divide(divide(X_54,divide(X_54,zero)),zero) = divide(X_54,divide(X_54,zero)) )
      | ( divide(divide(X_54,divide(X_54,zero)),zero) != zero ) ),
    inference(superposition,[status(thm),theory(equality)],[c_794,c_539]) ).

tff(c_894,plain,
    ! [X_55] : ( divide(X_55,divide(X_55,zero)) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_781,c_781,c_811]) ).

tff(c_972,plain,
    ! [X_55] : ( divide(X_55,zero) = X_55 ),
    inference(superposition,[status(thm),theory(equality)],[c_894,c_539]) ).

tff(c_237,plain,
    ! [X_33,X_16] : less_equal(divide(divide(X_33,X_16),zero),divide(divide(X_33,X_16),X_16)),
    inference(superposition,[status(thm),theory(equality)],[c_20,c_198]) ).

tff(c_1118,plain,
    ! [X_58,X_59] : less_equal(divide(X_58,X_59),divide(divide(X_58,X_59),X_59)),
    inference(demodulation,[status(thm),theory(equality)],[c_972,c_237]) ).

tff(c_176,plain,
    ! [X_5,Y_6] :
      ( ( divide(X_5,Y_6) = X_5 )
      | ~ less_equal(X_5,divide(X_5,Y_6)) ),
    inference(resolution,[status(thm)],[c_6,c_164]) ).

tff(c_1190,plain,
    ! [X_58,X_59] : ( divide(divide(X_58,X_59),X_59) = divide(X_58,X_59) ),
    inference(resolution,[status(thm)],[c_1118,c_176]) ).

tff(c_10,plain,
    ! [X_10] : less_equal(zero,X_10),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_22,plain,
    less_equal(divide(a,b),d),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_85,plain,
    ! [X_24,Y_25] :
      ( ( divide(X_24,Y_25) = zero )
      | ~ less_equal(X_24,Y_25) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_99,plain,
    divide(divide(a,b),d) = zero,
    inference(resolution,[status(thm)],[c_22,c_85]) ).

tff(c_12,plain,
    ! [Y_12,X_11] :
      ( ( Y_12 = X_11 )
      | ~ less_equal(Y_12,X_11)
      | ~ less_equal(X_11,Y_12) ),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_2655,plain,
    ! [X_81,Z_82,Y_83] :
      ( ( divide(divide(X_81,Z_82),divide(Y_83,Z_82)) = divide(divide(X_81,Y_83),Z_82) )
      | ~ less_equal(divide(divide(X_81,Y_83),Z_82),divide(divide(X_81,Z_82),divide(Y_83,Z_82))) ),
    inference(resolution,[status(thm)],[c_198,c_12]) ).

tff(c_2784,plain,
    ! [Z_82] :
      ( ( divide(divide(divide(a,b),Z_82),divide(d,Z_82)) = divide(divide(divide(a,b),d),Z_82) )
      | ~ less_equal(divide(zero,Z_82),divide(divide(divide(a,b),Z_82),divide(d,Z_82))) ),
    inference(superposition,[status(thm),theory(equality)],[c_99,c_2655]) ).

tff(c_2934,plain,
    ! [Z_84] : ( divide(divide(divide(a,b),Z_84),divide(d,Z_84)) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_10,c_18,c_18,c_99,c_2784]) ).

tff(c_3031,plain,
    divide(divide(a,b),divide(d,b)) = zero,
    inference(superposition,[status(thm),theory(equality)],[c_1190,c_2934]) ).

tff(c_271,plain,
    ! [X_33,Z_34,Y_35] :
      ( ( divide(divide(X_33,Z_34),divide(Y_35,Z_34)) = divide(divide(X_33,Y_35),Z_34) )
      | ~ less_equal(divide(divide(X_33,Y_35),Z_34),divide(divide(X_33,Z_34),divide(Y_35,Z_34))) ),
    inference(resolution,[status(thm)],[c_198,c_12]) ).

tff(c_3126,plain,
    ( ( divide(divide(a,b),divide(d,b)) = divide(divide(a,d),b) )
    | ~ less_equal(divide(divide(a,d),b),zero) ),
    inference(superposition,[status(thm),theory(equality)],[c_3031,c_271]) ).

tff(c_3209,plain,
    ( ( divide(divide(a,d),b) = zero )
    | ~ less_equal(divide(divide(a,d),b),zero) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3031,c_3126]) ).

tff(c_3210,plain,
    ~ less_equal(divide(divide(a,d),b),zero),
    inference(negUnitSimplification,[status(thm)],[c_112,c_3209]) ).

tff(c_231,plain,
    less_equal(divide(divide(a,d),divide(b,d)),zero),
    inference(superposition,[status(thm),theory(equality)],[c_99,c_198]) ).

tff(c_178,plain,
    ! [X_10] :
      ( ( zero = X_10 )
      | ~ less_equal(X_10,zero) ),
    inference(resolution,[status(thm)],[c_10,c_164]) ).

tff(c_562,plain,
    divide(divide(a,d),divide(b,d)) = zero,
    inference(resolution,[status(thm)],[c_231,c_178]) ).

tff(c_98,plain,
    ! [X_5,Y_6] : ( divide(divide(X_5,Y_6),X_5) = zero ),
    inference(resolution,[status(thm)],[c_6,c_85]) ).

tff(c_209,plain,
    ! [X_33,X_5,Y_6] : less_equal(divide(divide(X_33,X_5),zero),divide(divide(X_33,divide(X_5,Y_6)),X_5)),
    inference(superposition,[status(thm),theory(equality)],[c_98,c_198]) ).

tff(c_7149,plain,
    ! [X_119,X_120,Y_121] : less_equal(divide(X_119,X_120),divide(divide(X_119,divide(X_120,Y_121)),X_120)),
    inference(demodulation,[status(thm),theory(equality)],[c_972,c_209]) ).

tff(c_7353,plain,
    less_equal(divide(divide(a,d),b),divide(zero,b)),
    inference(superposition,[status(thm),theory(equality)],[c_562,c_7149]) ).

tff(c_7476,plain,
    less_equal(divide(divide(a,d),b),zero),
    inference(demodulation,[status(thm),theory(equality)],[c_18,c_7353]) ).

tff(c_7478,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3210,c_7476]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : HEN006-6 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14  % 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
% 0.14/0.35  % Computer : n005.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 13:08:27 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 5.99/2.54  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.01/2.55  
% 6.01/2.55  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.01/2.59  
% 6.01/2.59  Inference rules
% 6.01/2.59  ----------------------
% 6.01/2.59  #Ref     : 0
% 6.01/2.59  #Sup     : 1775
% 6.01/2.59  #Fact    : 0
% 6.01/2.59  #Define  : 0
% 6.01/2.59  #Split   : 1
% 6.01/2.59  #Chain   : 0
% 6.01/2.59  #Close   : 0
% 6.01/2.59  
% 6.01/2.59  Ordering : KBO
% 6.01/2.59  
% 6.01/2.59  Simplification rules
% 6.01/2.59  ----------------------
% 6.01/2.59  #Subsume      : 60
% 6.01/2.59  #Demod        : 2972
% 6.01/2.59  #Tautology    : 1410
% 6.01/2.59  #SimpNegUnit  : 2
% 6.01/2.59  #BackRed      : 17
% 6.01/2.59  
% 6.01/2.59  #Partial instantiations: 0
% 6.01/2.59  #Strategies tried      : 1
% 6.01/2.59  
% 6.01/2.59  Timing (in seconds)
% 6.01/2.59  ----------------------
% 6.01/2.59  Preprocessing        : 0.44
% 6.01/2.59  Parsing              : 0.25
% 6.01/2.59  CNF conversion       : 0.02
% 6.01/2.59  Main loop            : 0.98
% 6.01/2.59  Inferencing          : 0.33
% 6.01/2.59  Reduction            : 0.43
% 6.01/2.59  Demodulation         : 0.35
% 6.01/2.59  BG Simplification    : 0.03
% 6.01/2.59  Subsumption          : 0.14
% 6.01/2.59  Abstraction          : 0.04
% 6.01/2.59  MUC search           : 0.00
% 6.01/2.59  Cooper               : 0.00
% 6.01/2.59  Total                : 1.47
% 6.01/2.59  Index Insertion      : 0.00
% 6.01/2.59  Index Deletion       : 0.00
% 6.01/2.59  Index Matching       : 0.00
% 6.01/2.59  BG Taut test         : 0.00
%------------------------------------------------------------------------------