TSTP Solution File: HEN006-3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : HEN006-3 : 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 : n007.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 4.75s 2.27s
% Output   : CNFRefutation 4.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   68 (  37 unt;   7 typ;   0 def)
%            Number of atoms       :   91 (  48 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   64 (  34   ~;  30   |;   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   :   80 (;  80   !;   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_80,axiom,
    ~ less_equal(divide(a,d),b),
    file(unknown,unknown) ).

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

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

tff(f_62,axiom,
    ! [X] : less_equal(zero,X),
    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_78,axiom,
    less_equal(divide(a,b),d),
    file(unknown,unknown) ).

tff(c_77,plain,
    ! [X_22,Y_23] :
      ( less_equal(X_22,Y_23)
      | ( divide(X_22,Y_23) != zero ) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_18,plain,
    ~ less_equal(divide(a,d),b),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_85,plain,
    divide(divide(a,d),b) != zero,
    inference(resolution,[status(thm)],[c_77,c_18]) ).

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_22,plain,
    ! [X_18,Y_19] :
      ( ( divide(X_18,Y_19) = zero )
      | ~ less_equal(X_18,Y_19) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_35,plain,
    ! [X_5,Y_6] : ( divide(divide(X_5,Y_6),X_5) = zero ),
    inference(resolution,[status(thm)],[c_6,c_22]) ).

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

tff(c_37,plain,
    ! [X_10] : ( divide(zero,X_10) = zero ),
    inference(resolution,[status(thm)],[c_10,c_22]) ).

tff(c_171,plain,
    ! [X_30,Z_31,Y_32] : less_equal(divide(divide(X_30,Z_31),divide(Y_32,Z_31)),divide(divide(X_30,Y_32),Z_31)),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_586,plain,
    ! [X_46,Y_47] : less_equal(divide(divide(X_46,X_46),divide(Y_47,X_46)),zero),
    inference(superposition,[status(thm),theory(equality)],[c_35,c_171]) ).

tff(c_664,plain,
    ! [X_48] : less_equal(divide(divide(X_48,X_48),zero),zero),
    inference(superposition,[status(thm),theory(equality)],[c_35,c_586]) ).

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_125,plain,
    ! [Y_26,X_27] :
      ( ( Y_26 = X_27 )
      | ~ less_equal(Y_26,X_27)
      | ~ less_equal(X_27,Y_26) ),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_136,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_125]) ).

tff(c_667,plain,
    ! [X_48] :
      ( ( divide(divide(X_48,X_48),zero) = zero )
      | ( divide(zero,divide(divide(X_48,X_48),zero)) != zero ) ),
    inference(resolution,[status(thm)],[c_664,c_136]) ).

tff(c_702,plain,
    ! [X_49] : ( divide(divide(X_49,X_49),zero) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_37,c_667]) ).

tff(c_141,plain,
    ! [X_28] :
      ( ( zero = X_28 )
      | ~ less_equal(X_28,zero) ),
    inference(resolution,[status(thm)],[c_10,c_125]) ).

tff(c_154,plain,
    ! [X_3] :
      ( ( zero = X_3 )
      | ( divide(X_3,zero) != zero ) ),
    inference(resolution,[status(thm)],[c_4,c_141]) ).

tff(c_771,plain,
    ! [X_49] : ( divide(X_49,X_49) = zero ),
    inference(superposition,[status(thm),theory(equality)],[c_702,c_154]) ).

tff(c_2216,plain,
    ! [X_70,X_71] : less_equal(divide(divide(X_70,X_71),zero),divide(divide(X_70,zero),X_71)),
    inference(superposition,[status(thm),theory(equality)],[c_37,c_171]) ).

tff(c_2864,plain,
    ! [X_75] : less_equal(divide(divide(X_75,divide(X_75,zero)),zero),zero),
    inference(superposition,[status(thm),theory(equality)],[c_771,c_2216]) ).

tff(c_2867,plain,
    ! [X_75] :
      ( ( divide(divide(X_75,divide(X_75,zero)),zero) = zero )
      | ( divide(zero,divide(divide(X_75,divide(X_75,zero)),zero)) != zero ) ),
    inference(resolution,[status(thm)],[c_2864,c_136]) ).

tff(c_2922,plain,
    ! [X_76] : ( divide(divide(X_76,divide(X_76,zero)),zero) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_37,c_2867]) ).

tff(c_294,plain,
    ! [Y_37,X_38] :
      ( ( Y_37 = X_38 )
      | ~ less_equal(Y_37,X_38)
      | ( divide(X_38,Y_37) != zero ) ),
    inference(resolution,[status(thm)],[c_4,c_125]) ).

tff(c_314,plain,
    ! [Y_4,X_3] :
      ( ( Y_4 = X_3 )
      | ( divide(Y_4,X_3) != zero )
      | ( divide(X_3,Y_4) != zero ) ),
    inference(resolution,[status(thm)],[c_4,c_294]) ).

tff(c_2947,plain,
    ! [X_76] :
      ( ( divide(X_76,divide(X_76,zero)) = zero )
      | ( divide(zero,divide(X_76,divide(X_76,zero))) != zero ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2922,c_314]) ).

tff(c_3091,plain,
    ! [X_77] : ( divide(X_77,divide(X_77,zero)) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_37,c_2947]) ).

tff(c_3111,plain,
    ! [X_77] :
      ( ( divide(X_77,zero) = X_77 )
      | ( divide(divide(X_77,zero),X_77) != zero ) ),
    inference(superposition,[status(thm),theory(equality)],[c_3091,c_314]) ).

tff(c_3241,plain,
    ! [X_77] : ( divide(X_77,zero) = X_77 ),
    inference(demodulation,[status(thm),theory(equality)],[c_35,c_3111]) ).

tff(c_785,plain,
    ! [X_50] : ( divide(X_50,X_50) = zero ),
    inference(superposition,[status(thm),theory(equality)],[c_702,c_154]) ).

tff(c_8,plain,
    ! [X_7,Z_8,Y_9] : less_equal(divide(divide(X_7,Z_8),divide(Y_9,Z_8)),divide(divide(X_7,Y_9),Z_8)),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_831,plain,
    ! [X_7,X_50] : less_equal(divide(divide(X_7,X_50),zero),divide(divide(X_7,X_50),X_50)),
    inference(superposition,[status(thm),theory(equality)],[c_785,c_8]) ).

tff(c_3496,plain,
    ! [X_80,X_81] : less_equal(divide(X_80,X_81),divide(divide(X_80,X_81),X_81)),
    inference(demodulation,[status(thm),theory(equality)],[c_3241,c_831]) ).

tff(c_3499,plain,
    ! [X_80,X_81] :
      ( ( divide(divide(X_80,X_81),X_81) = divide(X_80,X_81) )
      | ( divide(divide(divide(X_80,X_81),X_81),divide(X_80,X_81)) != zero ) ),
    inference(resolution,[status(thm)],[c_3496,c_136]) ).

tff(c_3647,plain,
    ! [X_82,X_83] : ( divide(divide(X_82,X_83),X_83) = divide(X_82,X_83) ),
    inference(demodulation,[status(thm),theory(equality)],[c_35,c_3499]) ).

tff(c_16,plain,
    less_equal(divide(a,b),d),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_36,plain,
    divide(divide(a,b),d) = zero,
    inference(resolution,[status(thm)],[c_16,c_22]) ).

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_891,plain,
    ! [X_51,Z_52,Y_53] :
      ( ( divide(divide(X_51,Z_52),divide(Y_53,Z_52)) = divide(divide(X_51,Y_53),Z_52) )
      | ~ less_equal(divide(divide(X_51,Y_53),Z_52),divide(divide(X_51,Z_52),divide(Y_53,Z_52))) ),
    inference(resolution,[status(thm)],[c_171,c_12]) ).

tff(c_957,plain,
    ! [Z_52] :
      ( ( divide(divide(divide(a,b),Z_52),divide(d,Z_52)) = divide(divide(divide(a,b),d),Z_52) )
      | ~ less_equal(divide(zero,Z_52),divide(divide(divide(a,b),Z_52),divide(d,Z_52))) ),
    inference(superposition,[status(thm),theory(equality)],[c_36,c_891]) ).

tff(c_1022,plain,
    ! [Z_52] : ( divide(divide(divide(a,b),Z_52),divide(d,Z_52)) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_10,c_37,c_37,c_36,c_957]) ).

tff(c_3693,plain,
    divide(divide(a,b),divide(d,b)) = zero,
    inference(superposition,[status(thm),theory(equality)],[c_3647,c_1022]) ).

tff(c_227,plain,
    ! [X_30,Z_31,Y_32] :
      ( ( divide(divide(X_30,Z_31),divide(Y_32,Z_31)) = divide(divide(X_30,Y_32),Z_31) )
      | ~ less_equal(divide(divide(X_30,Y_32),Z_31),divide(divide(X_30,Z_31),divide(Y_32,Z_31))) ),
    inference(resolution,[status(thm)],[c_171,c_12]) ).

tff(c_3909,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_3693,c_227]) ).

tff(c_3969,plain,
    ( ( divide(divide(a,d),b) = zero )
    | ~ less_equal(divide(divide(a,d),b),zero) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3693,c_3909]) ).

tff(c_3970,plain,
    ~ less_equal(divide(divide(a,d),b),zero),
    inference(negUnitSimplification,[status(thm)],[c_85,c_3969]) ).

tff(c_960,plain,
    ( ( divide(divide(a,d),divide(b,d)) = divide(divide(a,b),d) )
    | ~ less_equal(zero,divide(divide(a,d),divide(b,d))) ),
    inference(superposition,[status(thm),theory(equality)],[c_36,c_891]) ).

tff(c_1024,plain,
    divide(divide(a,d),divide(b,d)) = zero,
    inference(demodulation,[status(thm),theory(equality)],[c_10,c_36,c_960]) ).

tff(c_182,plain,
    ! [X_30,X_5,Y_6] : less_equal(divide(divide(X_30,X_5),zero),divide(divide(X_30,divide(X_5,Y_6)),X_5)),
    inference(superposition,[status(thm),theory(equality)],[c_35,c_171]) ).

tff(c_3990,plain,
    ! [X_84,X_85,Y_86] : less_equal(divide(X_84,X_85),divide(divide(X_84,divide(X_85,Y_86)),X_85)),
    inference(demodulation,[status(thm),theory(equality)],[c_3241,c_182]) ).

tff(c_4078,plain,
    less_equal(divide(divide(a,d),b),divide(zero,b)),
    inference(superposition,[status(thm),theory(equality)],[c_1024,c_3990]) ).

tff(c_4175,plain,
    less_equal(divide(divide(a,d),b),zero),
    inference(demodulation,[status(thm),theory(equality)],[c_37,c_4078]) ).

tff(c_4177,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3970,c_4175]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : HEN006-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.15  % 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
% 0.14/0.36  % Computer : n007.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 12:57:23 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 4.75/2.27  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.75/2.28  
% 4.75/2.28  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.75/2.33  
% 4.75/2.33  Inference rules
% 4.75/2.33  ----------------------
% 4.75/2.33  #Ref     : 0
% 4.75/2.33  #Sup     : 993
% 4.75/2.33  #Fact    : 0
% 4.75/2.33  #Define  : 0
% 4.75/2.33  #Split   : 1
% 4.75/2.33  #Chain   : 0
% 4.75/2.33  #Close   : 0
% 4.75/2.33  
% 4.75/2.33  Ordering : KBO
% 4.75/2.33  
% 4.75/2.33  Simplification rules
% 4.75/2.33  ----------------------
% 4.75/2.33  #Subsume      : 58
% 4.75/2.33  #Demod        : 1387
% 4.75/2.33  #Tautology    : 705
% 4.75/2.33  #SimpNegUnit  : 2
% 4.75/2.33  #BackRed      : 14
% 4.75/2.33  
% 4.75/2.33  #Partial instantiations: 0
% 4.75/2.33  #Strategies tried      : 1
% 4.75/2.33  
% 4.75/2.33  Timing (in seconds)
% 4.75/2.33  ----------------------
% 4.75/2.34  Preprocessing        : 0.42
% 4.75/2.34  Parsing              : 0.22
% 4.75/2.34  CNF conversion       : 0.02
% 4.75/2.34  Main loop            : 0.78
% 4.75/2.34  Inferencing          : 0.28
% 4.75/2.34  Reduction            : 0.30
% 4.75/2.34  Demodulation         : 0.24
% 4.75/2.34  BG Simplification    : 0.03
% 4.75/2.34  Subsumption          : 0.12
% 4.75/2.34  Abstraction          : 0.04
% 4.75/2.34  MUC search           : 0.00
% 4.75/2.34  Cooper               : 0.00
% 4.75/2.34  Total                : 1.28
% 4.75/2.34  Index Insertion      : 0.00
% 4.75/2.34  Index Deletion       : 0.00
% 4.75/2.34  Index Matching       : 0.00
% 4.75/2.34  BG Taut test         : 0.00
%------------------------------------------------------------------------------