TSTP Solution File: HEN008-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : HEN008-1 : 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/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 10:42:17 EDT 2023

% Result   : Unsatisfiable 5.76s 2.41s
% Output   : CNFRefutation 6.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   52 (  21 unt;  10 typ;   0 def)
%            Number of atoms       :   81 (  11 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   80 (  41   ~;  39   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Maximal term depth    :    2 (   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   :   75 (;  75   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ quotient > less_equal > divide > #nlpp > zero > identity > c > bQc > b > aQc > 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(aQc,type,
    aQc: $i ).

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

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

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

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

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

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

tff(f_111,axiom,
    ~ less_equal(aQc,bQc),
    file(unknown,unknown) ).

tff(f_107,axiom,
    less_equal(a,b),
    file(unknown,unknown) ).

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

tff(f_95,axiom,
    ! [X,Y] : quotient(X,Y,divide(X,Y)),
    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_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_109,axiom,
    quotient(b,c,bQc),
    file(unknown,unknown) ).

tff(f_108,axiom,
    quotient(a,c,aQc),
    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_53,axiom,
    ! [X,Y] :
      ( ~ quotient(X,Y,zero)
      | less_equal(X,Y) ),
    file(unknown,unknown) ).

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

tff(c_20,plain,
    less_equal(a,b),
    inference(cnfTransformation,[status(thm)],[f_107]) ).

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_16,plain,
    ! [X_20,Y_21] : quotient(X_20,Y_21,divide(X_20,Y_21)),
    inference(cnfTransformation,[status(thm)],[f_95]) ).

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_281,plain,
    divide(a,b) = zero,
    inference(resolution,[status(thm)],[c_20,c_256]) ).

tff(c_332,plain,
    quotient(a,b,zero),
    inference(superposition,[status(thm),theory(equality)],[c_281,c_16]) ).

tff(c_30,plain,
    ! [Z_30,X_31,Y_32] :
      ( less_equal(Z_30,X_31)
      | ~ quotient(X_31,Y_32,Z_30) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_40,plain,
    ! [X_20,Y_21] : less_equal(divide(X_20,Y_21),X_20),
    inference(resolution,[status(thm)],[c_16,c_30]) ).

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_95,plain,
    ! [X_46] :
      ( ( zero = X_46 )
      | ~ less_equal(X_46,zero) ),
    inference(resolution,[status(thm)],[c_10,c_55]) ).

tff(c_104,plain,
    ! [Y_21] : ( divide(zero,Y_21) = zero ),
    inference(resolution,[status(thm)],[c_40,c_95]) ).

tff(c_24,plain,
    quotient(b,c,bQc),
    inference(cnfTransformation,[status(thm)],[f_109]) ).

tff(c_22,plain,
    quotient(a,c,aQc),
    inference(cnfTransformation,[status(thm)],[f_108]) ).

tff(c_107,plain,
    ! [X_51,V4_49,Y_53,V3_48,V2_47,Z_50,V5_54,V1_52] :
      ( less_equal(V4_49,V5_54)
      | ~ quotient(V1_52,Z_50,V5_54)
      | ~ quotient(V3_48,V2_47,V4_49)
      | ~ quotient(X_51,Z_50,V3_48)
      | ~ quotient(Y_53,Z_50,V2_47)
      | ~ quotient(X_51,Y_53,V1_52) ),
    inference(cnfTransformation,[status(thm)],[f_77]) ).

tff(c_917,plain,
    ! [V4_115,Y_109,X_110,V3_113,V2_114,Y_111,X_112] :
      ( less_equal(V4_115,divide(X_110,Y_109))
      | ~ quotient(V3_113,V2_114,V4_115)
      | ~ quotient(X_112,Y_109,V3_113)
      | ~ quotient(Y_111,Y_109,V2_114)
      | ~ quotient(X_112,Y_111,X_110) ),
    inference(resolution,[status(thm)],[c_16,c_107]) ).

tff(c_2865,plain,
    ! [X_222,X_223,Y_219,Y_220,X_224,Y_221] :
      ( less_equal(divide(X_222,Y_219),divide(X_223,Y_220))
      | ~ quotient(X_224,Y_220,X_222)
      | ~ quotient(Y_221,Y_220,Y_219)
      | ~ quotient(X_224,Y_221,X_223) ),
    inference(resolution,[status(thm)],[c_16,c_917]) ).

tff(c_2983,plain,
    ! [Y_229,X_230,Y_231] :
      ( less_equal(divide(aQc,Y_229),divide(X_230,c))
      | ~ quotient(Y_231,c,Y_229)
      | ~ quotient(a,Y_231,X_230) ),
    inference(resolution,[status(thm)],[c_22,c_2865]) ).

tff(c_3151,plain,
    ! [X_240] :
      ( less_equal(divide(aQc,bQc),divide(X_240,c))
      | ~ quotient(a,b,X_240) ),
    inference(resolution,[status(thm)],[c_24,c_2983]) ).

tff(c_3174,plain,
    ( less_equal(divide(aQc,bQc),zero)
    | ~ quotient(a,b,zero) ),
    inference(superposition,[status(thm),theory(equality)],[c_104,c_3151]) ).

tff(c_3180,plain,
    less_equal(divide(aQc,bQc),zero),
    inference(demodulation,[status(thm),theory(equality)],[c_332,c_3174]) ).

tff(c_72,plain,
    ! [X_16] :
      ( ( zero = X_16 )
      | ~ less_equal(X_16,zero) ),
    inference(resolution,[status(thm)],[c_10,c_55]) ).

tff(c_3232,plain,
    divide(aQc,bQc) = zero,
    inference(resolution,[status(thm)],[c_3180,c_72]) ).

tff(c_3258,plain,
    quotient(aQc,bQc,zero),
    inference(superposition,[status(thm),theory(equality)],[c_3232,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_3291,plain,
    less_equal(aQc,bQc),
    inference(resolution,[status(thm)],[c_3258,c_4]) ).

tff(c_3315,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_26,c_3291]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : HEN008-1 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.13  % 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 : n005.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 13:07:42 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 5.76/2.41  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.76/2.42  
% 5.76/2.42  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.04/2.45  
% 6.04/2.45  Inference rules
% 6.04/2.45  ----------------------
% 6.04/2.45  #Ref     : 0
% 6.04/2.45  #Sup     : 787
% 6.04/2.45  #Fact    : 0
% 6.04/2.45  #Define  : 0
% 6.04/2.45  #Split   : 22
% 6.04/2.45  #Chain   : 0
% 6.04/2.45  #Close   : 0
% 6.04/2.45  
% 6.04/2.45  Ordering : KBO
% 6.04/2.45  
% 6.04/2.45  Simplification rules
% 6.04/2.45  ----------------------
% 6.04/2.45  #Subsume      : 180
% 6.04/2.45  #Demod        : 430
% 6.04/2.45  #Tautology    : 417
% 6.04/2.45  #SimpNegUnit  : 2
% 6.04/2.45  #BackRed      : 2
% 6.04/2.45  
% 6.04/2.45  #Partial instantiations: 0
% 6.04/2.45  #Strategies tried      : 1
% 6.04/2.45  
% 6.04/2.45  Timing (in seconds)
% 6.04/2.45  ----------------------
% 6.04/2.45  Preprocessing        : 0.44
% 6.04/2.45  Parsing              : 0.25
% 6.04/2.45  CNF conversion       : 0.02
% 6.04/2.45  Main loop            : 0.92
% 6.04/2.45  Inferencing          : 0.35
% 6.04/2.45  Reduction            : 0.29
% 6.04/2.45  Demodulation         : 0.21
% 6.04/2.45  BG Simplification    : 0.03
% 6.04/2.45  Subsumption          : 0.20
% 6.04/2.45  Abstraction          : 0.03
% 6.04/2.45  MUC search           : 0.00
% 6.04/2.45  Cooper               : 0.00
% 6.04/2.45  Total                : 1.42
% 6.04/2.45  Index Insertion      : 0.00
% 6.04/2.45  Index Deletion       : 0.00
% 6.04/2.45  Index Matching       : 0.00
% 6.04/2.45  BG Taut test         : 0.00
%------------------------------------------------------------------------------