TSTP Solution File: HEN009-2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : HEN009-2 : 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 : n004.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 10:42:18 EDT 2023

% Result   : Unsatisfiable 6.72s 2.58s
% Output   : CNFRefutation 6.72s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   40 (  16 unt;   9 typ;   0 def)
%            Number of atoms       :   59 (   5 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   59 (  31   ~;  28   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    1 (   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    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   39 (;  39   !;   0   ?;   0   :)

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

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

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

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

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

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

tff(f_162,axiom,
    idQa != idQ__idQ_idQa,
    file(unknown,unknown) ).

tff(f_116,axiom,
    ! [X] : quotient(X,zero,X),
    file(unknown,unknown) ).

tff(f_60,axiom,
    ! [X,Y,Z] :
      ( ~ quotient(X,Y,Z)
      | less_equal(Z,X) ),
    file(unknown,unknown) ).

tff(f_159,axiom,
    quotient(identity,idQa,idQ_idQa),
    file(unknown,unknown) ).

tff(f_160,axiom,
    quotient(identity,idQ_idQa,idQ__idQ_idQa),
    file(unknown,unknown) ).

tff(f_135,axiom,
    ! [W1,Z,X,Y,W2] :
      ( ~ quotient(X,Y,W1)
      | ~ less_equal(W1,Z)
      | ~ quotient(X,Z,W2)
      | less_equal(W2,Y) ),
    file(unknown,unknown) ).

tff(f_90,axiom,
    ! [X,Y] :
      ( ~ less_equal(X,Y)
      | ~ less_equal(Y,X)
      | ( X = Y ) ),
    file(unknown,unknown) ).

tff(f_158,axiom,
    quotient(identity,a,idQa),
    file(unknown,unknown) ).

tff(f_146,axiom,
    ! [W1,Z,X,Y,W2] :
      ( ~ less_equal(X,Y)
      | ~ quotient(Z,Y,W1)
      | ~ quotient(Z,X,W2)
      | less_equal(W1,W2) ),
    file(unknown,unknown) ).

tff(c_42,plain,
    idQa != idQ__idQ_idQa,
    inference(cnfTransformation,[status(thm)],[f_162]) ).

tff(c_26,plain,
    ! [X_29] : quotient(X_29,zero,X_29),
    inference(cnfTransformation,[status(thm)],[f_116]) ).

tff(c_51,plain,
    ! [Z_58,X_59,Y_60] :
      ( less_equal(Z_58,X_59)
      | ~ quotient(X_59,Y_60,Z_58) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_90,plain,
    ! [X_29] : less_equal(X_29,X_29),
    inference(resolution,[status(thm)],[c_26,c_51]) ).

tff(c_38,plain,
    quotient(identity,idQa,idQ_idQa),
    inference(cnfTransformation,[status(thm)],[f_159]) ).

tff(c_40,plain,
    quotient(identity,idQ_idQa,idQ__idQ_idQa),
    inference(cnfTransformation,[status(thm)],[f_160]) ).

tff(c_621,plain,
    ! [Y_108,W2_106,X_107,W1_105,Z_109] :
      ( less_equal(W2_106,Y_108)
      | ~ quotient(X_107,Z_109,W2_106)
      | ~ less_equal(W1_105,Z_109)
      | ~ quotient(X_107,Y_108,W1_105) ),
    inference(cnfTransformation,[status(thm)],[f_135]) ).

tff(c_5479,plain,
    ! [Y_241,W1_242] :
      ( less_equal(idQ__idQ_idQa,Y_241)
      | ~ less_equal(W1_242,idQ_idQa)
      | ~ quotient(identity,Y_241,W1_242) ),
    inference(resolution,[status(thm)],[c_40,c_621]) ).

tff(c_5498,plain,
    ( less_equal(idQ__idQ_idQa,idQa)
    | ~ less_equal(idQ_idQa,idQ_idQa) ),
    inference(resolution,[status(thm)],[c_38,c_5479]) ).

tff(c_5521,plain,
    less_equal(idQ__idQ_idQa,idQa),
    inference(demodulation,[status(thm),theory(equality)],[c_90,c_5498]) ).

tff(c_12,plain,
    ! [Y_18,X_17] :
      ( ( Y_18 = X_17 )
      | ~ less_equal(Y_18,X_17)
      | ~ less_equal(X_17,Y_18) ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_5532,plain,
    ( ( idQa = idQ__idQ_idQa )
    | ~ less_equal(idQa,idQ__idQ_idQa) ),
    inference(resolution,[status(thm)],[c_5521,c_12]) ).

tff(c_5537,plain,
    ~ less_equal(idQa,idQ__idQ_idQa),
    inference(negUnitSimplification,[status(thm)],[c_42,c_5532]) ).

tff(c_36,plain,
    quotient(identity,a,idQa),
    inference(cnfTransformation,[status(thm)],[f_158]) ).

tff(c_1601,plain,
    ! [Y_151,W1_152] :
      ( less_equal(idQ_idQa,Y_151)
      | ~ less_equal(W1_152,idQa)
      | ~ quotient(identity,Y_151,W1_152) ),
    inference(resolution,[status(thm)],[c_38,c_621]) ).

tff(c_1627,plain,
    ( less_equal(idQ_idQa,a)
    | ~ less_equal(idQa,idQa) ),
    inference(resolution,[status(thm)],[c_36,c_1601]) ).

tff(c_1645,plain,
    less_equal(idQ_idQa,a),
    inference(demodulation,[status(thm),theory(equality)],[c_90,c_1627]) ).

tff(c_410,plain,
    ! [Z_93,X_95,W2_94,Y_97,W1_96] :
      ( less_equal(W1_96,W2_94)
      | ~ quotient(Z_93,X_95,W2_94)
      | ~ quotient(Z_93,Y_97,W1_96)
      | ~ less_equal(X_95,Y_97) ),
    inference(cnfTransformation,[status(thm)],[f_146]) ).

tff(c_8036,plain,
    ! [W1_282,Y_283] :
      ( less_equal(W1_282,idQ__idQ_idQa)
      | ~ quotient(identity,Y_283,W1_282)
      | ~ less_equal(idQ_idQa,Y_283) ),
    inference(resolution,[status(thm)],[c_40,c_410]) ).

tff(c_8062,plain,
    ( less_equal(idQa,idQ__idQ_idQa)
    | ~ less_equal(idQ_idQa,a) ),
    inference(resolution,[status(thm)],[c_36,c_8036]) ).

tff(c_8080,plain,
    less_equal(idQa,idQ__idQ_idQa),
    inference(demodulation,[status(thm),theory(equality)],[c_1645,c_8062]) ).

tff(c_8082,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_5537,c_8080]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : HEN009-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.12  % 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
% 0.12/0.33  % Computer : n004.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu Aug  3 13:04:41 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 6.72/2.58  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.72/2.58  
% 6.72/2.58  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.72/2.61  
% 6.72/2.61  Inference rules
% 6.72/2.61  ----------------------
% 6.72/2.61  #Ref     : 0
% 6.72/2.61  #Sup     : 1932
% 6.72/2.61  #Fact    : 0
% 6.72/2.61  #Define  : 0
% 6.72/2.61  #Split   : 6
% 6.72/2.61  #Chain   : 0
% 6.72/2.61  #Close   : 0
% 6.72/2.61  
% 6.72/2.61  Ordering : KBO
% 6.72/2.61  
% 6.72/2.61  Simplification rules
% 6.72/2.61  ----------------------
% 6.72/2.61  #Subsume      : 277
% 6.72/2.61  #Demod        : 1619
% 6.72/2.61  #Tautology    : 1393
% 6.72/2.61  #SimpNegUnit  : 29
% 6.72/2.61  #BackRed      : 0
% 6.72/2.61  
% 6.72/2.61  #Partial instantiations: 0
% 6.72/2.61  #Strategies tried      : 1
% 6.72/2.61  
% 6.72/2.61  Timing (in seconds)
% 6.72/2.61  ----------------------
% 6.72/2.61  Preprocessing        : 0.47
% 6.72/2.61  Parsing              : 0.23
% 6.72/2.62  CNF conversion       : 0.03
% 6.72/2.62  Main loop            : 1.11
% 6.72/2.62  Inferencing          : 0.40
% 6.72/2.62  Reduction            : 0.39
% 6.72/2.62  Demodulation         : 0.29
% 6.72/2.62  BG Simplification    : 0.03
% 6.72/2.62  Subsumption          : 0.22
% 6.72/2.62  Abstraction          : 0.04
% 6.72/2.62  MUC search           : 0.00
% 6.72/2.62  Cooper               : 0.00
% 6.72/2.62  Total                : 1.64
% 6.72/2.62  Index Insertion      : 0.00
% 6.72/2.62  Index Deletion       : 0.00
% 6.72/2.62  Index Matching       : 0.00
% 6.72/2.62  BG Taut test         : 0.00
%------------------------------------------------------------------------------