TSTP Solution File: GRP159-1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP159-1 : 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/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 10:40:19 EDT 2023

% Result   : Unsatisfiable 3.17s 1.82s
% Output   : CNFRefutation 3.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   25 (  17 unt;   8 typ;   0 def)
%            Number of atoms       :   17 (  16 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    3 (   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    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   20 (;  20   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ multiply > least_upper_bound > greatest_lower_bound > #nlpp > inverse > identity > c > 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(c,type,
    c: $i ).

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

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

tff(f_101,axiom,
    ! [X,Y] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = 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_106,axiom,
    ! [X,Y,Z] : ( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ),
    file(unknown,unknown) ).

tff(f_117,axiom,
    least_upper_bound(multiply(c,a),multiply(c,b)) != multiply(c,b),
    file(unknown,unknown) ).

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

tff(c_91,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_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_253,plain,
    ! [Y_51,X_52] : ( least_upper_bound(Y_51,greatest_lower_bound(X_52,Y_51)) = Y_51 ),
    inference(superposition,[status(thm),theory(equality)],[c_91,c_20]) ).

tff(c_291,plain,
    least_upper_bound(b,a) = b,
    inference(superposition,[status(thm),theory(equality)],[c_32,c_253]) ).

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_309,plain,
    least_upper_bound(a,b) = b,
    inference(superposition,[status(thm),theory(equality)],[c_291,c_10]) ).

tff(c_24,plain,
    ! [X_22,Y_23,Z_24] : ( least_upper_bound(multiply(X_22,Y_23),multiply(X_22,Z_24)) = multiply(X_22,least_upper_bound(Y_23,Z_24)) ),
    inference(cnfTransformation,[status(thm)],[f_106]) ).

tff(c_34,plain,
    least_upper_bound(multiply(c,a),multiply(c,b)) != multiply(c,b),
    inference(cnfTransformation,[status(thm)],[f_117]) ).

tff(c_35,plain,
    multiply(c,least_upper_bound(a,b)) != multiply(c,b),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_34]) ).

tff(c_338,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_309,c_35]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : GRP159-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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
% 0.16/0.37  % Computer : n005.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Thu Aug  3 22:09:12 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 3.17/1.82  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.17/1.82  
% 3.17/1.82  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.17/1.84  
% 3.17/1.84  Inference rules
% 3.17/1.84  ----------------------
% 3.17/1.84  #Ref     : 0
% 3.17/1.84  #Sup     : 78
% 3.17/1.84  #Fact    : 0
% 3.17/1.84  #Define  : 0
% 3.17/1.84  #Split   : 0
% 3.17/1.84  #Chain   : 0
% 3.17/1.84  #Close   : 0
% 3.17/1.84  
% 3.17/1.84  Ordering : KBO
% 3.17/1.84  
% 3.17/1.84  Simplification rules
% 3.17/1.84  ----------------------
% 3.17/1.84  #Subsume      : 0
% 3.17/1.84  #Demod        : 28
% 3.17/1.84  #Tautology    : 65
% 3.17/1.84  #SimpNegUnit  : 0
% 3.17/1.84  #BackRed      : 0
% 3.17/1.84  
% 3.17/1.84  #Partial instantiations: 0
% 3.17/1.84  #Strategies tried      : 1
% 3.17/1.84  
% 3.17/1.84  Timing (in seconds)
% 3.17/1.84  ----------------------
% 3.17/1.85  Preprocessing        : 0.47
% 3.17/1.85  Parsing              : 0.24
% 3.17/1.85  CNF conversion       : 0.02
% 3.17/1.85  Main loop            : 0.28
% 3.17/1.85  Inferencing          : 0.10
% 3.17/1.85  Reduction            : 0.10
% 3.17/1.85  Demodulation         : 0.08
% 3.17/1.85  BG Simplification    : 0.02
% 3.17/1.85  Subsumption          : 0.05
% 3.17/1.85  Abstraction          : 0.01
% 3.17/1.85  MUC search           : 0.00
% 3.17/1.85  Cooper               : 0.00
% 3.17/1.85  Total                : 0.80
% 3.17/1.85  Index Insertion      : 0.00
% 3.17/1.85  Index Deletion       : 0.00
% 3.17/1.85  Index Matching       : 0.00
% 3.17/1.85  BG Taut test         : 0.00
%------------------------------------------------------------------------------