TSTP Solution File: GRP169-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP169-1 : 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/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 : n011.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 10:40:21 EDT 2023

% Result   : Unsatisfiable 16.43s 7.03s
% Output   : CNFRefutation 16.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   17
% 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    :    5 (   2 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   :   63 (;  63   !;   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_120,axiom,
    least_upper_bound(a,b) != a,
    file(unknown,unknown) ).

tff(f_92,axiom,
    ! [X,Y] : ( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ),
    file(unknown,unknown) ).

tff(f_59,axiom,
    ! [X] : ( multiply(identity,X) = X ),
    file(unknown,unknown) ).

tff(f_63,axiom,
    ! [X] : ( multiply(inverse(X),X) = identity ),
    file(unknown,unknown) ).

tff(f_66,axiom,
    ! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
    file(unknown,unknown) ).

tff(f_118,axiom,
    least_upper_bound(inverse(a),inverse(b)) = inverse(b),
    file(unknown,unknown) ).

tff(f_109,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_106,axiom,
    ! [X,Y] : ( greatest_lower_bound(X,least_upper_bound(X,Y)) = X ),
    file(unknown,unknown) ).

tff(f_115,axiom,
    ! [Y,Z,X] : ( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) ),
    file(unknown,unknown) ).

tff(f_104,axiom,
    ! [X,Y] : ( least_upper_bound(X,greatest_lower_bound(X,Y)) = X ),
    file(unknown,unknown) ).

tff(c_34,plain,
    least_upper_bound(a,b) != a,
    inference(cnfTransformation,[status(thm)],[f_120]) ).

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_92]) ).

tff(c_2,plain,
    ! [X_1] : ( multiply(identity,X_1) = X_1 ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_4,plain,
    ! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_287,plain,
    ! [X_50,Y_51,Z_52] : ( multiply(multiply(X_50,Y_51),Z_52) = multiply(X_50,multiply(Y_51,Z_52)) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_302,plain,
    ! [X_2,Z_52] : ( multiply(inverse(X_2),multiply(X_2,Z_52)) = multiply(identity,Z_52) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_287]) ).

tff(c_310,plain,
    ! [X_2,Z_52] : ( multiply(inverse(X_2),multiply(X_2,Z_52)) = Z_52 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_302]) ).

tff(c_312,plain,
    ! [X_53,Z_54] : ( multiply(inverse(X_53),multiply(X_53,Z_54)) = Z_54 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_302]) ).

tff(c_1079,plain,
    ! [X_77,Z_78] : ( multiply(inverse(inverse(X_77)),Z_78) = multiply(X_77,Z_78) ),
    inference(superposition,[status(thm),theory(equality)],[c_310,c_312]) ).

tff(c_333,plain,
    ! [X_2] : ( multiply(inverse(inverse(X_2)),identity) = X_2 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_312]) ).

tff(c_1096,plain,
    ! [X_77] : ( multiply(X_77,identity) = X_77 ),
    inference(superposition,[status(thm),theory(equality)],[c_1079,c_333]) ).

tff(c_6,plain,
    ! [X_3,Y_4,Z_5] : ( multiply(multiply(X_3,Y_4),Z_5) = multiply(X_3,multiply(Y_4,Z_5)) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_1139,plain,
    ! [X_79] : ( multiply(X_79,identity) = X_79 ),
    inference(superposition,[status(thm),theory(equality)],[c_1079,c_333]) ).

tff(c_324,plain,
    ! [X_2,Z_52] : ( multiply(inverse(inverse(X_2)),Z_52) = multiply(X_2,Z_52) ),
    inference(superposition,[status(thm),theory(equality)],[c_310,c_312]) ).

tff(c_1146,plain,
    ! [X_2] : ( inverse(inverse(X_2)) = multiply(X_2,identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_1139,c_324]) ).

tff(c_1205,plain,
    ! [X_2] : ( inverse(inverse(X_2)) = X_2 ),
    inference(demodulation,[status(thm),theory(equality)],[c_1096,c_1146]) ).

tff(c_32,plain,
    least_upper_bound(inverse(a),inverse(b)) = inverse(b),
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_1219,plain,
    ! [X_80,Y_81,Z_82] : ( least_upper_bound(multiply(X_80,Y_81),multiply(X_80,Z_82)) = multiply(X_80,least_upper_bound(Y_81,Z_82)) ),
    inference(cnfTransformation,[status(thm)],[f_109]) ).

tff(c_22,plain,
    ! [X_20,Y_21] : ( greatest_lower_bound(X_20,least_upper_bound(X_20,Y_21)) = X_20 ),
    inference(cnfTransformation,[status(thm)],[f_106]) ).

tff(c_22891,plain,
    ! [X_268,Y_269,Z_270] : ( greatest_lower_bound(multiply(X_268,Y_269),multiply(X_268,least_upper_bound(Y_269,Z_270))) = multiply(X_268,Y_269) ),
    inference(superposition,[status(thm),theory(equality)],[c_1219,c_22]) ).

tff(c_23257,plain,
    ! [X_2,Z_270] : ( greatest_lower_bound(identity,multiply(inverse(X_2),least_upper_bound(X_2,Z_270))) = multiply(inverse(X_2),X_2) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_22891]) ).

tff(c_26051,plain,
    ! [X_286,Z_287] : ( greatest_lower_bound(identity,multiply(inverse(X_286),least_upper_bound(X_286,Z_287))) = identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_23257]) ).

tff(c_26309,plain,
    greatest_lower_bound(identity,multiply(inverse(inverse(a)),inverse(b))) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_32,c_26051]) ).

tff(c_26381,plain,
    greatest_lower_bound(identity,multiply(a,inverse(b))) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_1205,c_26309]) ).

tff(c_1360,plain,
    ! [Y_84,X_85,Z_86] : ( greatest_lower_bound(multiply(Y_84,X_85),multiply(Z_86,X_85)) = multiply(greatest_lower_bound(Y_84,Z_86),X_85) ),
    inference(cnfTransformation,[status(thm)],[f_115]) ).

tff(c_1432,plain,
    ! [Z_86,X_1] : ( multiply(greatest_lower_bound(identity,Z_86),X_1) = greatest_lower_bound(X_1,multiply(Z_86,X_1)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_1360]) ).

tff(c_26403,plain,
    ! [X_1] : ( greatest_lower_bound(X_1,multiply(multiply(a,inverse(b)),X_1)) = multiply(identity,X_1) ),
    inference(superposition,[status(thm),theory(equality)],[c_26381,c_1432]) ).

tff(c_48566,plain,
    ! [X_388] : ( greatest_lower_bound(X_388,multiply(a,multiply(inverse(b),X_388))) = X_388 ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_2,c_26403]) ).

tff(c_48822,plain,
    greatest_lower_bound(b,multiply(a,identity)) = b,
    inference(superposition,[status(thm),theory(equality)],[c_4,c_48566]) ).

tff(c_48875,plain,
    greatest_lower_bound(a,b) = b,
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_1096,c_48822]) ).

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_104]) ).

tff(c_49479,plain,
    least_upper_bound(a,b) = a,
    inference(superposition,[status(thm),theory(equality)],[c_48875,c_20]) ).

tff(c_49511,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_34,c_49479]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : GRP169-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.15  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.14/0.38  % Computer : n011.cluster.edu
% 0.14/0.38  % Model    : x86_64 x86_64
% 0.14/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38  % Memory   : 8042.1875MB
% 0.14/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.38  % CPULimit : 300
% 0.14/0.38  % WCLimit  : 300
% 0.14/0.38  % DateTime : Thu Aug  3 22:04:36 EDT 2023
% 0.14/0.38  % CPUTime  : 
% 16.43/7.03  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.43/7.04  
% 16.43/7.04  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.43/7.07  
% 16.43/7.07  Inference rules
% 16.43/7.07  ----------------------
% 16.43/7.07  #Ref     : 0
% 16.43/7.07  #Sup     : 12590
% 16.43/7.07  #Fact    : 0
% 16.43/7.07  #Define  : 0
% 16.43/7.07  #Split   : 0
% 16.43/7.07  #Chain   : 0
% 16.43/7.07  #Close   : 0
% 16.43/7.07  
% 16.43/7.07  Ordering : KBO
% 16.43/7.07  
% 16.43/7.07  Simplification rules
% 16.43/7.07  ----------------------
% 16.43/7.07  #Subsume      : 215
% 16.43/7.07  #Demod        : 14896
% 16.43/7.07  #Tautology    : 7412
% 16.43/7.07  #SimpNegUnit  : 1
% 16.43/7.07  #BackRed      : 17
% 16.43/7.07  
% 16.43/7.07  #Partial instantiations: 0
% 16.43/7.07  #Strategies tried      : 1
% 16.52/7.07  
% 16.52/7.07  Timing (in seconds)
% 16.52/7.07  ----------------------
% 16.52/7.07  Preprocessing        : 0.49
% 16.52/7.07  Parsing              : 0.26
% 16.52/7.07  CNF conversion       : 0.02
% 16.52/7.07  Main loop            : 5.42
% 16.52/7.07  Inferencing          : 0.97
% 16.52/7.07  Reduction            : 3.07
% 16.52/7.07  Demodulation         : 2.80
% 16.52/7.07  BG Simplification    : 0.11
% 16.52/7.07  Subsumption          : 0.99
% 16.52/7.07  Abstraction          : 0.17
% 16.52/7.07  MUC search           : 0.00
% 16.52/7.07  Cooper               : 0.00
% 16.52/7.07  Total                : 5.96
% 16.52/7.07  Index Insertion      : 0.00
% 16.52/7.07  Index Deletion       : 0.00
% 16.52/7.07  Index Matching       : 0.00
% 16.52/7.07  BG Taut test         : 0.00
%------------------------------------------------------------------------------