TSTP Solution File: HEN006-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : HEN006-1 : 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/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 : n014.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 10:42:14 EDT 2023

% Result   : Unsatisfiable 76.25s 61.26s
% Output   : CNFRefutation 76.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   63 (  27 unt;  10 typ;   0 def)
%            Number of atoms       :  107 (  13 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  110 (  56   ~;  54   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   3   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :  104 (; 104   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ quotient > less_equal > divide > #nlpp > zero > z > y > xQz > xQy > x > identity

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

tff(f_111,axiom,
    ~ less_equal(xQz,y),
    file(unknown,unknown) ).

tff(f_95,axiom,
    ! [X,Y] : quotient(X,Y,divide(X,Y)),
    file(unknown,unknown) ).

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

tff(f_80,axiom,
    ! [X] : less_equal(zero,X),
    file(unknown,unknown) ).

tff(f_89,axiom,
    ! [X,Y] :
      ( ~ less_equal(X,Y)
      | ~ less_equal(Y,X)
      | ( X = Y ) ),
    file(unknown,unknown) ).

tff(f_108,axiom,
    less_equal(xQy,z),
    file(unknown,unknown) ).

tff(f_107,axiom,
    quotient(x,y,xQy),
    file(unknown,unknown) ).

tff(f_109,axiom,
    quotient(x,z,xQz),
    file(unknown,unknown) ).

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

tff(f_77,axiom,
    ! [V3,V5,Z,V1,X,Y,V2,V4] :
      ( ~ quotient(X,Y,V1)
      | ~ quotient(Y,Z,V2)
      | ~ quotient(X,Z,V3)
      | ~ quotient(V3,V2,V4)
      | ~ quotient(V1,Z,V5)
      | less_equal(V4,V5) ),
    file(unknown,unknown) ).

tff(f_104,axiom,
    ! [X,Y,Z,W] :
      ( ~ quotient(X,Y,Z)
      | ~ quotient(X,Y,W)
      | ( Z = W ) ),
    file(unknown,unknown) ).

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

tff(c_26,plain,
    ~ less_equal(xQz,y),
    inference(cnfTransformation,[status(thm)],[f_111]) ).

tff(c_16,plain,
    ! [X_20,Y_21] : quotient(X_20,Y_21,divide(X_20,Y_21)),
    inference(cnfTransformation,[status(thm)],[f_95]) ).

tff(c_31,plain,
    ! [Z_32,X_33,Y_34] :
      ( less_equal(Z_32,X_33)
      | ~ quotient(X_33,Y_34,Z_32) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_41,plain,
    ! [X_20,Y_21] : less_equal(divide(X_20,Y_21),X_20),
    inference(resolution,[status(thm)],[c_16,c_31]) ).

tff(c_10,plain,
    ! [X_16] : less_equal(zero,X_16),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_55,plain,
    ! [Y_39,X_40] :
      ( ( Y_39 = X_40 )
      | ~ less_equal(Y_39,X_40)
      | ~ less_equal(X_40,Y_39) ),
    inference(cnfTransformation,[status(thm)],[f_89]) ).

tff(c_94,plain,
    ! [X_46] :
      ( ( zero = X_46 )
      | ~ less_equal(X_46,zero) ),
    inference(resolution,[status(thm)],[c_10,c_55]) ).

tff(c_103,plain,
    ! [Y_21] : ( divide(zero,Y_21) = zero ),
    inference(resolution,[status(thm)],[c_41,c_94]) ).

tff(c_22,plain,
    less_equal(xQy,z),
    inference(cnfTransformation,[status(thm)],[f_108]) ).

tff(c_20,plain,
    quotient(x,y,xQy),
    inference(cnfTransformation,[status(thm)],[f_107]) ).

tff(c_24,plain,
    quotient(x,z,xQz),
    inference(cnfTransformation,[status(thm)],[f_109]) ).

tff(c_2,plain,
    ! [X_1,Y_2] :
      ( quotient(X_1,Y_2,zero)
      | ~ less_equal(X_1,Y_2) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_134,plain,
    ! [V1_54,V3_50,Y_55,X_53,V4_51,V2_49,V5_56,Z_52] :
      ( less_equal(V4_51,V5_56)
      | ~ quotient(V1_54,Z_52,V5_56)
      | ~ quotient(V3_50,V2_49,V4_51)
      | ~ quotient(X_53,Z_52,V3_50)
      | ~ quotient(Y_55,Z_52,V2_49)
      | ~ quotient(X_53,Y_55,V1_54) ),
    inference(cnfTransformation,[status(thm)],[f_77]) ).

tff(c_1253,plain,
    ! [Y_131,V2_127,V4_130,X_132,V3_128,Y_133,X_129] :
      ( less_equal(V4_130,zero)
      | ~ quotient(V3_128,V2_127,V4_130)
      | ~ quotient(X_132,Y_133,V3_128)
      | ~ quotient(Y_131,Y_133,V2_127)
      | ~ quotient(X_132,Y_131,X_129)
      | ~ less_equal(X_129,Y_133) ),
    inference(resolution,[status(thm)],[c_2,c_134]) ).

tff(c_2719,plain,
    ! [Y_227,X_232,Y_228,Y_231,X_229,X_230] :
      ( less_equal(divide(X_229,Y_227),zero)
      | ~ quotient(X_230,Y_228,X_229)
      | ~ quotient(Y_231,Y_228,Y_227)
      | ~ quotient(X_230,Y_231,X_232)
      | ~ less_equal(X_232,Y_228) ),
    inference(resolution,[status(thm)],[c_16,c_1253]) ).

tff(c_260033,plain,
    ! [Y_2379,Y_2380,X_2381] :
      ( less_equal(divide(xQz,Y_2379),zero)
      | ~ quotient(Y_2380,z,Y_2379)
      | ~ quotient(x,Y_2380,X_2381)
      | ~ less_equal(X_2381,z) ),
    inference(resolution,[status(thm)],[c_24,c_2719]) ).

tff(c_262367,plain,
    ! [X_2448,X_2449] :
      ( less_equal(divide(xQz,divide(X_2448,z)),zero)
      | ~ quotient(x,X_2448,X_2449)
      | ~ less_equal(X_2449,z) ),
    inference(resolution,[status(thm)],[c_16,c_260033]) ).

tff(c_262380,plain,
    ( less_equal(divide(xQz,divide(y,z)),zero)
    | ~ less_equal(xQy,z) ),
    inference(resolution,[status(thm)],[c_20,c_262367]) ).

tff(c_262395,plain,
    less_equal(divide(xQz,divide(y,z)),zero),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_262380]) ).

tff(c_73,plain,
    ! [X_16] :
      ( ( zero = X_16 )
      | ~ less_equal(X_16,zero) ),
    inference(resolution,[status(thm)],[c_10,c_55]) ).

tff(c_262421,plain,
    divide(xQz,divide(y,z)) = zero,
    inference(resolution,[status(thm)],[c_262395,c_73]) ).

tff(c_262469,plain,
    quotient(xQz,divide(y,z),zero),
    inference(superposition,[status(thm),theory(equality)],[c_262421,c_16]) ).

tff(c_81,plain,
    ! [Z_42,W_43,X_44,Y_45] :
      ( ( Z_42 = W_43 )
      | ~ quotient(X_44,Y_45,W_43)
      | ~ quotient(X_44,Y_45,Z_42) ),
    inference(cnfTransformation,[status(thm)],[f_104]) ).

tff(c_231,plain,
    ! [X_61,Y_62,Z_63] :
      ( ( divide(X_61,Y_62) = Z_63 )
      | ~ quotient(X_61,Y_62,Z_63) ),
    inference(resolution,[status(thm)],[c_16,c_81]) ).

tff(c_256,plain,
    ! [X_64,Y_65] :
      ( ( divide(X_64,Y_65) = zero )
      | ~ less_equal(X_64,Y_65) ),
    inference(resolution,[status(thm)],[c_2,c_231]) ).

tff(c_275,plain,
    ! [X_20,Y_21] : ( divide(divide(X_20,Y_21),X_20) = zero ),
    inference(resolution,[status(thm)],[c_41,c_256]) ).

tff(c_890,plain,
    ! [X_108,V3_110,V2_109,Y_112,V4_111,X_113,Y_107] :
      ( less_equal(V4_111,divide(X_108,Y_107))
      | ~ quotient(V3_110,V2_109,V4_111)
      | ~ quotient(X_113,Y_107,V3_110)
      | ~ quotient(Y_112,Y_107,V2_109)
      | ~ quotient(X_113,Y_112,X_108) ),
    inference(resolution,[status(thm)],[c_16,c_134]) ).

tff(c_2608,plain,
    ! [Y_222,X_221,Y_220,X_218,X_219,Y_217] :
      ( less_equal(divide(X_218,Y_217),divide(X_219,Y_222))
      | ~ quotient(X_221,Y_222,X_218)
      | ~ quotient(Y_220,Y_222,Y_217)
      | ~ quotient(X_221,Y_220,X_219) ),
    inference(resolution,[status(thm)],[c_16,c_890]) ).

tff(c_260324,plain,
    ! [Y_2393,X_2392,X_2391,Y_2394,Y_2390] :
      ( less_equal(divide(divide(X_2391,Y_2390),Y_2394),divide(X_2392,Y_2390))
      | ~ quotient(Y_2393,Y_2390,Y_2394)
      | ~ quotient(X_2391,Y_2393,X_2392) ),
    inference(resolution,[status(thm)],[c_16,c_2608]) ).

tff(c_369289,plain,
    ! [X_3259,Y_3260,X_3261,X_3262] :
      ( less_equal(divide(divide(X_3259,Y_3260),divide(X_3261,Y_3260)),divide(X_3262,Y_3260))
      | ~ quotient(X_3259,X_3261,X_3262) ),
    inference(resolution,[status(thm)],[c_16,c_260324]) ).

tff(c_581137,plain,
    ! [X_4487,X_4488,X_4489,Y_4490] :
      ( less_equal(divide(divide(X_4487,X_4488),zero),divide(X_4489,X_4488))
      | ~ quotient(X_4487,divide(X_4488,Y_4490),X_4489) ),
    inference(superposition,[status(thm),theory(equality)],[c_275,c_369289]) ).

tff(c_581328,plain,
    less_equal(divide(divide(xQz,y),zero),divide(zero,y)),
    inference(resolution,[status(thm)],[c_262469,c_581137]) ).

tff(c_581454,plain,
    less_equal(divide(divide(xQz,y),zero),zero),
    inference(demodulation,[status(thm),theory(equality)],[c_103,c_581328]) ).

tff(c_581507,plain,
    divide(divide(xQz,y),zero) = zero,
    inference(resolution,[status(thm)],[c_581454,c_73]) ).

tff(c_581821,plain,
    quotient(divide(xQz,y),zero,zero),
    inference(superposition,[status(thm),theory(equality)],[c_581507,c_16]) ).

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

tff(c_581995,plain,
    less_equal(divide(xQz,y),zero),
    inference(resolution,[status(thm)],[c_581821,c_4]) ).

tff(c_582015,plain,
    divide(xQz,y) = zero,
    inference(resolution,[status(thm)],[c_581995,c_73]) ).

tff(c_582531,plain,
    quotient(xQz,y,zero),
    inference(superposition,[status(thm),theory(equality)],[c_582015,c_16]) ).

tff(c_582724,plain,
    less_equal(xQz,y),
    inference(resolution,[status(thm)],[c_582531,c_4]) ).

tff(c_582764,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_26,c_582724]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : HEN006-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % 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
% 0.17/0.35  % Computer : n014.cluster.edu
% 0.17/0.35  % Model    : x86_64 x86_64
% 0.17/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35  % Memory   : 8042.1875MB
% 0.17/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35  % CPULimit : 300
% 0.17/0.35  % WCLimit  : 300
% 0.17/0.35  % DateTime : Thu Aug  3 13:05:03 EDT 2023
% 0.17/0.35  % CPUTime  : 
% 76.25/61.26  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 76.25/61.27  
% 76.25/61.27  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 76.35/61.31  
% 76.35/61.31  Inference rules
% 76.35/61.31  ----------------------
% 76.35/61.31  #Ref     : 0
% 76.35/61.31  #Sup     : 138745
% 76.35/61.31  #Fact    : 0
% 76.35/61.31  #Define  : 0
% 76.35/61.31  #Split   : 217
% 76.35/61.31  #Chain   : 0
% 76.35/61.31  #Close   : 0
% 76.35/61.31  
% 76.35/61.31  Ordering : KBO
% 76.35/61.31  
% 76.35/61.31  Simplification rules
% 76.35/61.31  ----------------------
% 76.35/61.31  #Subsume      : 29696
% 76.35/61.31  #Demod        : 128932
% 76.35/61.31  #Tautology    : 84635
% 76.35/61.31  #SimpNegUnit  : 1
% 76.35/61.31  #BackRed      : 496
% 76.35/61.31  
% 76.35/61.31  #Partial instantiations: 0
% 76.35/61.31  #Strategies tried      : 1
% 76.35/61.31  
% 76.35/61.31  Timing (in seconds)
% 76.35/61.31  ----------------------
% 76.35/61.31  Preprocessing        : 0.55
% 76.35/61.31  Parsing              : 0.30
% 76.35/61.31  CNF conversion       : 0.04
% 76.35/61.31  Main loop            : 59.68
% 76.35/61.31  Inferencing          : 7.74
% 76.35/61.31  Reduction            : 29.20
% 76.35/61.31  Demodulation         : 22.88
% 76.35/61.31  BG Simplification    : 0.36
% 76.35/61.31  Subsumption          : 20.54
% 76.35/61.31  Abstraction          : 0.62
% 76.35/61.31  MUC search           : 0.00
% 76.35/61.31  Cooper               : 0.00
% 76.35/61.31  Total                : 60.29
% 76.35/61.31  Index Insertion      : 0.00
% 76.35/61.31  Index Deletion       : 0.00
% 76.35/61.31  Index Matching       : 0.00
% 76.35/61.31  BG Taut test         : 0.00
%------------------------------------------------------------------------------