TSTP Solution File: GRP172-2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP172-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 : n024.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 10:40:22 EDT 2023

% Result   : Unsatisfiable 8.82s 3.15s
% Output   : CNFRefutation 8.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   50 (  43 unt;   7 typ;   0 def)
%            Number of atoms       :   43 (  42 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   64 (;  64   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ multiply > least_upper_bound > greatest_lower_bound > #nlpp > inverse > identity > b > a

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(a,type,
    a: $i ).

tff(inverse,type,
    inverse: $i > $i ).

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

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

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

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

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

tff(f_118,axiom,
    least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
    file(unknown,unknown) ).

tff(f_116,axiom,
    greatest_lower_bound(identity,b) = identity,
    file(unknown,unknown) ).

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

tff(f_115,axiom,
    greatest_lower_bound(identity,a) = identity,
    file(unknown,unknown) ).

tff(f_101,axiom,
    ! [X,Y] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
    file(unknown,unknown) ).

tff(f_56,axiom,
    ! [X] : ( multiply(identity,X) = X ),
    file(unknown,unknown) ).

tff(f_110,axiom,
    ! [Y,Z,X] : ( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ),
    file(unknown,unknown) ).

tff(f_91,axiom,
    ! [X,Y] : ( least_upper_bound(X,Y) = least_upper_bound(Y,X) ),
    file(unknown,unknown) ).

tff(f_103,axiom,
    ! [X,Y] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
    file(unknown,unknown) ).

tff(f_93,axiom,
    ! [X,Y,Z] : ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ),
    file(unknown,unknown) ).

tff(f_97,axiom,
    ! [X] : ( least_upper_bound(X,X) = X ),
    file(unknown,unknown) ).

tff(f_95,axiom,
    ! [X,Y,Z] : ( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ),
    file(unknown,unknown) ).

tff(c_36,plain,
    least_upper_bound(identity,multiply(a,b)) != multiply(a,b),
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_34,plain,
    greatest_lower_bound(identity,b) = identity,
    inference(cnfTransformation,[status(thm)],[f_116]) ).

tff(c_112,plain,
    ! [Y_40,X_41] : ( greatest_lower_bound(Y_40,X_41) = greatest_lower_bound(X_41,Y_40) ),
    inference(cnfTransformation,[status(thm)],[f_89]) ).

tff(c_32,plain,
    greatest_lower_bound(identity,a) = identity,
    inference(cnfTransformation,[status(thm)],[f_115]) ).

tff(c_127,plain,
    greatest_lower_bound(a,identity) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_112,c_32]) ).

tff(c_200,plain,
    ! [X_44,Y_45] : ( least_upper_bound(X_44,greatest_lower_bound(X_44,Y_45)) = X_44 ),
    inference(cnfTransformation,[status(thm)],[f_101]) ).

tff(c_218,plain,
    least_upper_bound(a,identity) = a,
    inference(superposition,[status(thm),theory(equality)],[c_127,c_200]) ).

tff(c_2,plain,
    ! [X_1] : ( multiply(identity,X_1) = X_1 ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_1263,plain,
    ! [Y_77,X_78,Z_79] : ( least_upper_bound(multiply(Y_77,X_78),multiply(Z_79,X_78)) = multiply(least_upper_bound(Y_77,Z_79),X_78) ),
    inference(cnfTransformation,[status(thm)],[f_110]) ).

tff(c_10666,plain,
    ! [Y_167,X_168] : ( multiply(least_upper_bound(Y_167,identity),X_168) = least_upper_bound(multiply(Y_167,X_168),X_168) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_1263]) ).

tff(c_10,plain,
    ! [Y_9,X_8] : ( least_upper_bound(Y_9,X_8) = least_upper_bound(X_8,Y_9) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

tff(c_173,plain,
    ! [X_42,Y_43] : ( greatest_lower_bound(X_42,least_upper_bound(X_42,Y_43)) = X_42 ),
    inference(cnfTransformation,[status(thm)],[f_103]) ).

tff(c_182,plain,
    ! [X_8,Y_9] : ( greatest_lower_bound(X_8,least_upper_bound(Y_9,X_8)) = X_8 ),
    inference(superposition,[status(thm),theory(equality)],[c_10,c_173]) ).

tff(c_10928,plain,
    ! [X_169,Y_170] : ( greatest_lower_bound(X_169,multiply(least_upper_bound(Y_170,identity),X_169)) = X_169 ),
    inference(superposition,[status(thm),theory(equality)],[c_10666,c_182]) ).

tff(c_11114,plain,
    ! [X_171] : ( greatest_lower_bound(X_171,multiply(a,X_171)) = X_171 ),
    inference(superposition,[status(thm),theory(equality)],[c_218,c_10928]) ).

tff(c_681,plain,
    ! [X_59,Y_60,Z_61] : ( greatest_lower_bound(greatest_lower_bound(X_59,Y_60),Z_61) = greatest_lower_bound(X_59,greatest_lower_bound(Y_60,Z_61)) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_777,plain,
    ! [Z_61] : ( greatest_lower_bound(identity,greatest_lower_bound(b,Z_61)) = greatest_lower_bound(identity,Z_61) ),
    inference(superposition,[status(thm),theory(equality)],[c_34,c_681]) ).

tff(c_11170,plain,
    greatest_lower_bound(identity,multiply(a,b)) = greatest_lower_bound(identity,b),
    inference(superposition,[status(thm),theory(equality)],[c_11114,c_777]) ).

tff(c_11234,plain,
    greatest_lower_bound(identity,multiply(a,b)) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_34,c_11170]) ).

tff(c_8,plain,
    ! [Y_7,X_6] : ( greatest_lower_bound(Y_7,X_6) = greatest_lower_bound(X_6,Y_7) ),
    inference(cnfTransformation,[status(thm)],[f_89]) ).

tff(c_16,plain,
    ! [X_16] : ( least_upper_bound(X_16,X_16) = X_16 ),
    inference(cnfTransformation,[status(thm)],[f_97]) ).

tff(c_20,plain,
    ! [X_18,Y_19] : ( least_upper_bound(X_18,greatest_lower_bound(X_18,Y_19)) = X_18 ),
    inference(cnfTransformation,[status(thm)],[f_101]) ).

tff(c_367,plain,
    ! [X_50,Y_51,Z_52] : ( least_upper_bound(least_upper_bound(X_50,Y_51),Z_52) = least_upper_bound(X_50,least_upper_bound(Y_51,Z_52)) ),
    inference(cnfTransformation,[status(thm)],[f_95]) ).

tff(c_419,plain,
    ! [X_18,Y_19,Z_52] : ( least_upper_bound(X_18,least_upper_bound(greatest_lower_bound(X_18,Y_19),Z_52)) = least_upper_bound(X_18,Z_52) ),
    inference(superposition,[status(thm),theory(equality)],[c_20,c_367]) ).

tff(c_3553,plain,
    ! [Y_115,X_116,Y_117] : ( least_upper_bound(Y_115,least_upper_bound(X_116,Y_117)) = least_upper_bound(X_116,least_upper_bound(Y_117,Y_115)) ),
    inference(superposition,[status(thm),theory(equality)],[c_10,c_367]) ).

tff(c_4333,plain,
    ! [X_122,X_123] : ( least_upper_bound(X_122,least_upper_bound(X_123,X_122)) = least_upper_bound(X_123,X_122) ),
    inference(superposition,[status(thm),theory(equality)],[c_16,c_3553]) ).

tff(c_4474,plain,
    ! [Z_52,Y_19] : ( least_upper_bound(greatest_lower_bound(Z_52,Y_19),Z_52) = least_upper_bound(Z_52,Z_52) ),
    inference(superposition,[status(thm),theory(equality)],[c_419,c_4333]) ).

tff(c_4716,plain,
    ! [Z_124,Y_125] : ( least_upper_bound(greatest_lower_bound(Z_124,Y_125),Z_124) = Z_124 ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_4474]) ).

tff(c_4855,plain,
    ! [Y_7,X_6] : ( least_upper_bound(greatest_lower_bound(Y_7,X_6),X_6) = X_6 ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_4716]) ).

tff(c_12791,plain,
    least_upper_bound(identity,multiply(a,b)) = multiply(a,b),
    inference(superposition,[status(thm),theory(equality)],[c_11234,c_4855]) ).

tff(c_12831,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_36,c_12791]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : GRP172-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.13/0.15  % 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
% 0.15/0.36  % Computer : n024.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
% 0.22/0.36  % CPULimit : 300
% 0.22/0.36  % WCLimit  : 300
% 0.22/0.36  % DateTime : Thu Aug  3 22:08:30 EDT 2023
% 0.22/0.36  % CPUTime  : 
% 8.82/3.15  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.82/3.16  
% 8.82/3.16  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.94/3.19  
% 8.94/3.19  Inference rules
% 8.94/3.19  ----------------------
% 8.94/3.19  #Ref     : 0
% 8.94/3.19  #Sup     : 3209
% 8.94/3.19  #Fact    : 0
% 8.94/3.19  #Define  : 0
% 8.94/3.19  #Split   : 0
% 8.94/3.19  #Chain   : 0
% 8.94/3.19  #Close   : 0
% 8.94/3.19  
% 8.94/3.19  Ordering : KBO
% 8.94/3.19  
% 8.94/3.19  Simplification rules
% 8.94/3.19  ----------------------
% 8.94/3.19  #Subsume      : 104
% 8.94/3.19  #Demod        : 3015
% 8.94/3.19  #Tautology    : 1919
% 8.94/3.19  #SimpNegUnit  : 1
% 8.94/3.19  #BackRed      : 4
% 8.94/3.19  
% 8.94/3.19  #Partial instantiations: 0
% 8.94/3.19  #Strategies tried      : 1
% 8.94/3.19  
% 8.94/3.19  Timing (in seconds)
% 8.94/3.19  ----------------------
% 8.94/3.20  Preprocessing        : 0.45
% 8.94/3.20  Parsing              : 0.24
% 8.94/3.20  CNF conversion       : 0.02
% 8.94/3.20  Main loop            : 1.66
% 8.94/3.20  Inferencing          : 0.46
% 8.94/3.20  Reduction            : 0.82
% 8.94/3.20  Demodulation         : 0.71
% 8.94/3.20  BG Simplification    : 0.05
% 8.94/3.20  Subsumption          : 0.24
% 8.94/3.20  Abstraction          : 0.06
% 8.94/3.20  MUC search           : 0.00
% 8.94/3.20  Cooper               : 0.00
% 8.94/3.20  Total                : 2.16
% 8.94/3.20  Index Insertion      : 0.00
% 8.94/3.20  Index Deletion       : 0.00
% 8.94/3.20  Index Matching       : 0.00
% 8.94/3.20  BG Taut test         : 0.00
%------------------------------------------------------------------------------