TSTP Solution File: HEN010-3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : HEN010-3 : 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/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 : n015.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 10:42:19 EDT 2023

% Result   : Unsatisfiable 36.08s 23.21s
% Output   : CNFRefutation 36.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   70 (  37 unt;   5 typ;   0 def)
%            Number of atoms       :   99 (  63 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   70 (  36   ~;  34   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    6 (   2 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    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :  137 (; 137   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ less_equal > divide > #nlpp > zero > identity > 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(identity,type,
    identity: $i ).

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

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

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

tff(f_56,axiom,
    ! [X,Y] : less_equal(divide(X,Y),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_53,axiom,
    ! [X,Y] :
      ( ( divide(X,Y) != zero )
      | less_equal(X,Y) ),
    file(unknown,unknown) ).

tff(f_79,axiom,
    divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
    file(unknown,unknown) ).

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

tff(c_20,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_31,plain,
    ! [X_10] : ( divide(zero,X_10) = zero ),
    inference(resolution,[status(thm)],[c_10,c_20]) ).

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_30,plain,
    ! [X_5,Y_6] : ( divide(divide(X_5,Y_6),X_5) = zero ),
    inference(resolution,[status(thm)],[c_6,c_20]) ).

tff(c_191,plain,
    ! [X_34,Z_35,Y_36] : less_equal(divide(divide(X_34,Z_35),divide(Y_36,Z_35)),divide(divide(X_34,Y_36),Z_35)),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

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_785,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_191,c_12]) ).

tff(c_832,plain,
    ! [X_5,Y_6,Z_52] :
      ( ( divide(divide(divide(X_5,Y_6),Z_52),divide(X_5,Z_52)) = divide(divide(divide(X_5,Y_6),X_5),Z_52) )
      | ~ less_equal(divide(zero,Z_52),divide(divide(divide(X_5,Y_6),Z_52),divide(X_5,Z_52))) ),
    inference(superposition,[status(thm),theory(equality)],[c_30,c_785]) ).

tff(c_895,plain,
    ! [X_5,Y_6,Z_52] : ( divide(divide(divide(X_5,Y_6),Z_52),divide(X_5,Z_52)) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_10,c_31,c_31,c_30,c_832]) ).

tff(c_380,plain,
    ! [X_43,Y_44] : less_equal(divide(divide(X_43,X_43),divide(Y_44,X_43)),zero),
    inference(superposition,[status(thm),theory(equality)],[c_30,c_191]) ).

tff(c_433,plain,
    ! [X_45] : less_equal(divide(divide(X_45,X_45),zero),zero),
    inference(superposition,[status(thm),theory(equality)],[c_30,c_380]) ).

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_103,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_112,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_103]) ).

tff(c_436,plain,
    ! [X_45] :
      ( ( divide(divide(X_45,X_45),zero) = zero )
      | ( divide(zero,divide(divide(X_45,X_45),zero)) != zero ) ),
    inference(resolution,[status(thm)],[c_433,c_112]) ).

tff(c_471,plain,
    ! [X_46] : ( divide(divide(X_46,X_46),zero) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_31,c_436]) ).

tff(c_116,plain,
    ! [X_28] :
      ( ( zero = X_28 )
      | ~ less_equal(X_28,zero) ),
    inference(resolution,[status(thm)],[c_10,c_103]) ).

tff(c_129,plain,
    ! [X_3] :
      ( ( zero = X_3 )
      | ( divide(X_3,zero) != zero ) ),
    inference(resolution,[status(thm)],[c_4,c_116]) ).

tff(c_527,plain,
    ! [X_46] : ( divide(X_46,X_46) = zero ),
    inference(superposition,[status(thm),theory(equality)],[c_471,c_129]) ).

tff(c_1536,plain,
    ! [X_67,X_68] : less_equal(divide(divide(X_67,X_68),zero),divide(divide(X_67,zero),X_68)),
    inference(superposition,[status(thm),theory(equality)],[c_31,c_191]) ).

tff(c_2551,plain,
    ! [X_75] : less_equal(divide(divide(X_75,divide(X_75,zero)),zero),zero),
    inference(superposition,[status(thm),theory(equality)],[c_527,c_1536]) ).

tff(c_2554,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_2551,c_112]) ).

tff(c_2610,plain,
    ! [X_76] : ( divide(divide(X_76,divide(X_76,zero)),zero) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_31,c_2554]) ).

tff(c_246,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_103]) ).

tff(c_263,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_246]) ).

tff(c_2653,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_2610,c_263]) ).

tff(c_2791,plain,
    ! [X_77] : ( divide(X_77,divide(X_77,zero)) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_31,c_2653]) ).

tff(c_2825,plain,
    ! [X_77] :
      ( ( divide(X_77,zero) = X_77 )
      | ( divide(divide(X_77,zero),X_77) != zero ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2791,c_263]) ).

tff(c_2939,plain,
    ! [X_77] : ( divide(X_77,zero) = X_77 ),
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_2825]) ).

tff(c_202,plain,
    ! [X_34,X_5,Y_6] : less_equal(divide(divide(X_34,X_5),zero),divide(divide(X_34,divide(X_5,Y_6)),X_5)),
    inference(superposition,[status(thm),theory(equality)],[c_30,c_191]) ).

tff(c_3170,plain,
    ! [X_80,X_81,Y_82] : less_equal(divide(X_80,X_81),divide(divide(X_80,divide(X_81,Y_82)),X_81)),
    inference(demodulation,[status(thm),theory(equality)],[c_2939,c_202]) ).

tff(c_3173,plain,
    ! [X_80,X_81,Y_82] :
      ( ( divide(divide(X_80,divide(X_81,Y_82)),X_81) = divide(X_80,X_81) )
      | ( divide(divide(divide(X_80,divide(X_81,Y_82)),X_81),divide(X_80,X_81)) != zero ) ),
    inference(resolution,[status(thm)],[c_3170,c_112]) ).

tff(c_4408,plain,
    ! [X_94,X_95,Y_96] : ( divide(divide(X_94,divide(X_95,Y_96)),X_95) = divide(X_94,X_95) ),
    inference(demodulation,[status(thm),theory(equality)],[c_895,c_3173]) ).

tff(c_4663,plain,
    ! [X_97,X_98,Y_99] : less_equal(divide(X_97,X_98),divide(X_97,divide(X_98,Y_99))),
    inference(superposition,[status(thm),theory(equality)],[c_4408,c_6]) ).

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

tff(c_4788,plain,
    ! [X_97,X_98,Y_99] : ( divide(divide(X_97,X_98),divide(X_97,divide(X_98,Y_99))) = zero ),
    inference(resolution,[status(thm)],[c_4663,c_2]) ).

tff(c_236,plain,
    ! [X_34,Z_35,Y_36] : ( divide(divide(divide(X_34,Z_35),divide(Y_36,Z_35)),divide(divide(X_34,Y_36),Z_35)) = zero ),
    inference(resolution,[status(thm)],[c_191,c_2]) ).

tff(c_797,plain,
    ! [X_51,X_34,Y_36,Z_35] :
      ( ( divide(divide(X_51,divide(divide(X_34,Y_36),Z_35)),divide(divide(divide(X_34,Z_35),divide(Y_36,Z_35)),divide(divide(X_34,Y_36),Z_35))) = divide(divide(X_51,divide(divide(X_34,Z_35),divide(Y_36,Z_35))),divide(divide(X_34,Y_36),Z_35)) )
      | ~ less_equal(divide(divide(X_51,divide(divide(X_34,Z_35),divide(Y_36,Z_35))),divide(divide(X_34,Y_36),Z_35)),divide(divide(X_51,divide(divide(X_34,Y_36),Z_35)),zero)) ),
    inference(superposition,[status(thm),theory(equality)],[c_236,c_785]) ).

tff(c_876,plain,
    ! [X_51,X_34,Z_35,Y_36] :
      ( ( divide(divide(X_51,divide(divide(X_34,Z_35),divide(Y_36,Z_35))),divide(divide(X_34,Y_36),Z_35)) = divide(divide(X_51,divide(divide(X_34,Y_36),Z_35)),zero) )
      | ~ less_equal(divide(divide(X_51,divide(divide(X_34,Z_35),divide(Y_36,Z_35))),divide(divide(X_34,Y_36),Z_35)),divide(divide(X_51,divide(divide(X_34,Y_36),Z_35)),zero)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_236,c_797]) ).

tff(c_44326,plain,
    ! [X_251,X_252,Z_253,Y_254] :
      ( ( divide(divide(X_251,divide(divide(X_252,Z_253),divide(Y_254,Z_253))),divide(divide(X_252,Y_254),Z_253)) = divide(X_251,divide(divide(X_252,Y_254),Z_253)) )
      | ~ less_equal(divide(divide(X_251,divide(divide(X_252,Z_253),divide(Y_254,Z_253))),divide(divide(X_252,Y_254),Z_253)),divide(X_251,divide(divide(X_252,Y_254),Z_253))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2939,c_2939,c_876]) ).

tff(c_45376,plain,
    ! [X_252,Y_99,X_98] :
      ( ( divide(divide(divide(divide(X_252,Y_99),X_98),divide(divide(X_252,Y_99),divide(X_98,Y_99))),divide(divide(X_252,X_98),Y_99)) = divide(divide(divide(X_252,Y_99),X_98),divide(divide(X_252,X_98),Y_99)) )
      | ~ less_equal(divide(zero,divide(divide(X_252,X_98),Y_99)),divide(divide(divide(X_252,Y_99),X_98),divide(divide(X_252,X_98),Y_99))) ),
    inference(superposition,[status(thm),theory(equality)],[c_4788,c_44326]) ).

tff(c_46274,plain,
    ! [X_252,Y_99,X_98] : ( divide(divide(divide(X_252,Y_99),X_98),divide(divide(X_252,X_98),Y_99)) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_10,c_31,c_31,c_4788,c_45376]) ).

tff(c_47748,plain,
    ! [X_258,Y_259,X_260] : ( divide(divide(divide(X_258,Y_259),X_260),divide(divide(X_258,X_260),Y_259)) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_10,c_31,c_31,c_4788,c_45376]) ).

tff(c_48257,plain,
    ! [X_258,Y_259,X_260] :
      ( ( divide(divide(X_258,Y_259),X_260) = divide(divide(X_258,X_260),Y_259) )
      | ( divide(divide(divide(X_258,X_260),Y_259),divide(divide(X_258,Y_259),X_260)) != zero ) ),
    inference(superposition,[status(thm),theory(equality)],[c_47748,c_263]) ).

tff(c_49354,plain,
    ! [X_261,Y_262,X_263] : ( divide(divide(X_261,Y_262),X_263) = divide(divide(X_261,X_263),Y_262) ),
    inference(demodulation,[status(thm),theory(equality)],[c_46274,c_48257]) ).

tff(c_804,plain,
    ! [X_51,Y_53] :
      ( ( divide(divide(X_51,divide(X_51,Y_53)),divide(Y_53,divide(X_51,Y_53))) = divide(divide(X_51,Y_53),divide(X_51,Y_53)) )
      | ~ less_equal(zero,divide(divide(X_51,divide(X_51,Y_53)),divide(Y_53,divide(X_51,Y_53)))) ),
    inference(superposition,[status(thm),theory(equality)],[c_527,c_785]) ).

tff(c_10196,plain,
    ! [X_136,Y_137] : ( divide(divide(X_136,divide(X_136,Y_137)),divide(Y_137,divide(X_136,Y_137))) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_10,c_527,c_804]) ).

tff(c_3276,plain,
    ! [X_80,X_81,Y_82] : ( divide(divide(X_80,divide(X_81,Y_82)),X_81) = divide(X_80,X_81) ),
    inference(demodulation,[status(thm),theory(equality)],[c_895,c_3173]) ).

tff(c_10328,plain,
    ! [X_136,Y_137] : ( divide(divide(X_136,divide(X_136,Y_137)),Y_137) = divide(zero,Y_137) ),
    inference(superposition,[status(thm),theory(equality)],[c_10196,c_3276]) ).

tff(c_10669,plain,
    ! [X_136,Y_137] : ( divide(divide(X_136,divide(X_136,Y_137)),Y_137) = zero ),
    inference(demodulation,[status(thm),theory(equality)],[c_31,c_10328]) ).

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_21204,plain,
    ! [X_183,Z_184,Y_185] :
      ( ( divide(divide(X_183,Z_184),divide(Y_185,Z_184)) = divide(divide(X_183,Y_185),Z_184) )
      | ( divide(divide(divide(X_183,Y_185),Z_184),divide(divide(X_183,Z_184),divide(Y_185,Z_184))) != zero ) ),
    inference(resolution,[status(thm)],[c_8,c_246]) ).

tff(c_21355,plain,
    ! [X_183,Y_137,X_136] :
      ( ( divide(divide(X_183,Y_137),divide(divide(X_136,divide(X_136,Y_137)),Y_137)) = divide(divide(X_183,divide(X_136,divide(X_136,Y_137))),Y_137) )
      | ( divide(divide(divide(X_183,divide(X_136,divide(X_136,Y_137))),Y_137),divide(divide(X_183,Y_137),zero)) != zero ) ),
    inference(superposition,[status(thm),theory(equality)],[c_10669,c_21204]) ).

tff(c_21780,plain,
    ! [X_183,X_136,Y_137] : ( divide(divide(X_183,divide(X_136,divide(X_136,Y_137))),Y_137) = divide(X_183,Y_137) ),
    inference(demodulation,[status(thm),theory(equality)],[c_895,c_2939,c_2939,c_10669,c_21355]) ).

tff(c_49625,plain,
    ! [X_261,Y_262,X_136] : ( divide(divide(X_261,Y_262),divide(X_136,divide(X_136,Y_262))) = divide(X_261,Y_262) ),
    inference(superposition,[status(thm),theory(equality)],[c_49354,c_21780]) ).

tff(c_16,plain,
    divide(divide(identity,a),divide(identity,divide(identity,a))) != divide(identity,a),
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_220242,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_49625,c_16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : HEN010-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.15  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.15/0.36  % Computer : n015.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 13:25:14 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 36.08/23.21  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.08/23.22  
% 36.08/23.22  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 36.19/23.26  
% 36.19/23.26  Inference rules
% 36.19/23.26  ----------------------
% 36.19/23.26  #Ref     : 0
% 36.19/23.26  #Sup     : 53147
% 36.19/23.26  #Fact    : 0
% 36.19/23.26  #Define  : 0
% 36.19/23.26  #Split   : 3
% 36.19/23.26  #Chain   : 0
% 36.19/23.26  #Close   : 0
% 36.19/23.26  
% 36.19/23.26  Ordering : KBO
% 36.19/23.26  
% 36.19/23.26  Simplification rules
% 36.19/23.26  ----------------------
% 36.19/23.26  #Subsume      : 2635
% 36.19/23.26  #Demod        : 97987
% 36.19/23.26  #Tautology    : 36368
% 36.19/23.26  #SimpNegUnit  : 59
% 36.19/23.26  #BackRed      : 56
% 36.19/23.26  
% 36.19/23.26  #Partial instantiations: 0
% 36.19/23.26  #Strategies tried      : 1
% 36.19/23.26  
% 36.19/23.26  Timing (in seconds)
% 36.19/23.26  ----------------------
% 36.19/23.26  Preprocessing        : 0.40
% 36.19/23.26  Parsing              : 0.22
% 36.19/23.26  CNF conversion       : 0.02
% 36.19/23.26  Main loop            : 21.78
% 36.19/23.26  Inferencing          : 2.11
% 36.19/23.26  Reduction            : 16.17
% 36.19/23.26  Demodulation         : 15.44
% 36.19/23.26  BG Simplification    : 0.14
% 36.19/23.26  Subsumption          : 2.61
% 36.19/23.26  Abstraction          : 0.36
% 36.19/23.26  MUC search           : 0.00
% 36.19/23.26  Cooper               : 0.00
% 36.19/23.26  Total                : 22.24
% 36.19/23.26  Index Insertion      : 0.00
% 36.19/23.26  Index Deletion       : 0.00
% 36.19/23.26  Index Matching       : 0.00
% 36.19/23.26  BG Taut test         : 0.00
%------------------------------------------------------------------------------