TSTP Solution File: GRP087-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP087-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 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 : n009.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 10:39:48 EDT 2023

% Result   : Unsatisfiable 139.24s 113.89s
% Output   : CNFRefutation 139.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   59 (  44 unt;  11 typ;   0 def)
%            Number of atoms       :   57 (  55 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   25 (  16   ~;   9   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   9 con; 0-2 aty)
%            Number of variables   :   95 (;  95   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > c3 > b4 > b3 > b2 > b1 > a4 > a3 > a2 > a1

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(a1,type,
    a1: $i ).

tff(a3,type,
    a3: $i ).

tff(c3,type,
    c3: $i ).

tff(b2,type,
    b2: $i ).

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

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

tff(b1,type,
    b1: $i ).

tff(b4,type,
    b4: $i ).

tff(b3,type,
    b3: $i ).

tff(a2,type,
    a2: $i ).

tff(a4,type,
    a4: $i ).

tff(f_25,axiom,
    ! [X,Y,Z] : ( multiply(X,multiply(multiply(inverse(multiply(X,Y)),Z),Y)) = Z ),
    file(unknown,unknown) ).

tff(f_36,axiom,
    ( ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1) )
    | ( multiply(multiply(inverse(b2),b2),a2) != a2 )
    | ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
    | ( multiply(a4,b4) != multiply(b4,a4) ) ),
    file(unknown,unknown) ).

tff(c_2,plain,
    ! [X_1,Y_2,Z_3] : ( multiply(X_1,multiply(multiply(inverse(multiply(X_1,Y_2)),Z_3),Y_2)) = Z_3 ),
    inference(cnfTransformation,[status(thm)],[f_25]) ).

tff(c_5,plain,
    ! [X_4,Y_5,Z_6] : ( multiply(X_4,multiply(multiply(inverse(multiply(X_4,Y_5)),Z_6),Y_5)) = Z_6 ),
    inference(cnfTransformation,[status(thm)],[f_25]) ).

tff(c_28,plain,
    ! [X_7,Z_8,Z_9,Y_10] : ( multiply(X_7,multiply(multiply(inverse(Z_8),Z_9),multiply(multiply(inverse(multiply(X_7,Y_10)),Z_8),Y_10))) = Z_9 ),
    inference(superposition,[status(thm),theory(equality)],[c_5,c_2]) ).

tff(c_78,plain,
    ! [Z_3,Z_9] : ( multiply(multiply(inverse(Z_3),Z_9),Z_3) = Z_9 ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_28]) ).

tff(c_81,plain,
    ! [Z_11,Z_12] : ( multiply(multiply(inverse(Z_11),Z_12),Z_11) = Z_12 ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_28]) ).

tff(c_104,plain,
    ! [Z_13,Z_14,Z_15] : ( multiply(multiply(inverse(Z_13),Z_14),multiply(multiply(inverse(Z_14),Z_15),Z_13)) = Z_15 ),
    inference(superposition,[status(thm),theory(equality)],[c_81,c_2]) ).

tff(c_129,plain,
    ! [Z_3,Z_9] : ( multiply(multiply(inverse(Z_3),Z_3),Z_9) = Z_9 ),
    inference(superposition,[status(thm),theory(equality)],[c_78,c_104]) ).

tff(c_18583,plain,
    ! [X_153,Y_154,Y_155,Z_156] : ( multiply(multiply(inverse(multiply(inverse(multiply(X_153,Y_154)),Y_155)),Z_156),Y_155) = multiply(X_153,multiply(Z_156,Y_154)) ),
    inference(superposition,[status(thm),theory(equality)],[c_5,c_2]) ).

tff(c_18665,plain,
    ! [X_157,Y_158,Z_159] : ( multiply(inverse(multiply(X_157,Y_158)),multiply(X_157,multiply(Z_159,Y_158))) = Z_159 ),
    inference(superposition,[status(thm),theory(equality)],[c_18583,c_2]) ).

tff(c_18746,plain,
    ! [Z_9,Z_3,Z_159] : ( multiply(inverse(Z_9),multiply(multiply(inverse(Z_3),Z_3),multiply(Z_159,Z_9))) = Z_159 ),
    inference(superposition,[status(thm),theory(equality)],[c_129,c_18665]) ).

tff(c_18800,plain,
    ! [Z_9,Z_159] : ( multiply(inverse(Z_9),multiply(Z_159,Z_9)) = Z_159 ),
    inference(demodulation,[status(thm),theory(equality)],[c_129,c_18746]) ).

tff(c_18805,plain,
    ! [Z_160,Z_161] : ( multiply(inverse(Z_160),multiply(Z_161,Z_160)) = Z_161 ),
    inference(demodulation,[status(thm),theory(equality)],[c_129,c_18746]) ).

tff(c_18912,plain,
    ! [Z_162,Z_163] : ( multiply(inverse(multiply(inverse(Z_162),Z_162)),Z_163) = Z_163 ),
    inference(superposition,[status(thm),theory(equality)],[c_18805,c_2]) ).

tff(c_18926,plain,
    ! [Z_159,Z_162] : ( multiply(Z_159,multiply(inverse(Z_162),Z_162)) = Z_159 ),
    inference(superposition,[status(thm),theory(equality)],[c_18912,c_18800]) ).

tff(c_19031,plain,
    ! [Z_164,Z_165] : ( multiply(Z_164,multiply(inverse(Z_165),Z_165)) = Z_164 ),
    inference(superposition,[status(thm),theory(equality)],[c_18912,c_18800]) ).

tff(c_19135,plain,
    ! [X_1,Z_165,Z_3] : ( multiply(X_1,multiply(inverse(multiply(X_1,multiply(inverse(Z_165),Z_165))),Z_3)) = Z_3 ),
    inference(superposition,[status(thm),theory(equality)],[c_19031,c_2]) ).

tff(c_19198,plain,
    ! [X_166,Z_167] : ( multiply(X_166,multiply(inverse(X_166),Z_167)) = Z_167 ),
    inference(demodulation,[status(thm),theory(equality)],[c_18926,c_19135]) ).

tff(c_19303,plain,
    ! [Z_9,Z_159] : ( multiply(Z_9,Z_159) = multiply(Z_159,Z_9) ),
    inference(superposition,[status(thm),theory(equality)],[c_18800,c_19198]) ).

tff(c_18861,plain,
    ! [Z_161,X_1,Y_2] : ( multiply(Z_161,multiply(X_1,Y_2)) = multiply(X_1,multiply(Z_161,Y_2)) ),
    inference(superposition,[status(thm),theory(equality)],[c_18805,c_2]) ).

tff(c_236,plain,
    ! [Z_18,Y_19,Z_20] : ( multiply(multiply(inverse(multiply(inverse(Z_18),Y_19)),Z_20),Y_19) = multiply(Z_20,Z_18) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_81]) ).

tff(c_290,plain,
    ! [Z_21,Z_22] : ( multiply(inverse(Z_21),multiply(Z_22,Z_21)) = Z_22 ),
    inference(superposition,[status(thm),theory(equality)],[c_236,c_2]) ).

tff(c_333,plain,
    ! [Z_21,Z_3] : ( multiply(inverse(multiply(inverse(Z_21),Z_21)),Z_3) = Z_3 ),
    inference(superposition,[status(thm),theory(equality)],[c_290,c_2]) ).

tff(c_367,plain,
    ! [Z_23,Z_24] : ( multiply(inverse(multiply(inverse(Z_23),Z_23)),Z_24) = Z_24 ),
    inference(superposition,[status(thm),theory(equality)],[c_290,c_2]) ).

tff(c_258,plain,
    ! [Z_18,Z_20] : ( multiply(inverse(Z_18),multiply(Z_20,Z_18)) = Z_20 ),
    inference(superposition,[status(thm),theory(equality)],[c_236,c_2]) ).

tff(c_457,plain,
    ! [Z_25,Z_26] : ( multiply(Z_25,multiply(inverse(Z_26),Z_26)) = Z_25 ),
    inference(superposition,[status(thm),theory(equality)],[c_367,c_258]) ).

tff(c_90,plain,
    ! [Z_11,Z_12,Z_3] : ( multiply(multiply(inverse(Z_11),Z_12),multiply(multiply(inverse(Z_12),Z_3),Z_11)) = Z_3 ),
    inference(superposition,[status(thm),theory(equality)],[c_81,c_2]) ).

tff(c_511,plain,
    ! [Z_26,Z_12,Z_3] : ( multiply(multiply(inverse(multiply(inverse(Z_26),Z_26)),Z_12),multiply(inverse(Z_12),Z_3)) = Z_3 ),
    inference(superposition,[status(thm),theory(equality)],[c_457,c_90]) ).

tff(c_599,plain,
    ! [Z_27,Z_28] : ( multiply(Z_27,multiply(inverse(Z_27),Z_28)) = Z_28 ),
    inference(demodulation,[status(thm),theory(equality)],[c_333,c_511]) ).

tff(c_621,plain,
    ! [Z_28] : ( inverse(inverse(Z_28)) = Z_28 ),
    inference(superposition,[status(thm),theory(equality)],[c_599,c_258]) ).

tff(c_336,plain,
    ! [Z_20,Z_18] : ( multiply(inverse(multiply(Z_20,Z_18)),Z_20) = inverse(Z_18) ),
    inference(superposition,[status(thm),theory(equality)],[c_258,c_290]) ).

tff(c_4430,plain,
    ! [Z_73,Z_74] : ( multiply(inverse(multiply(Z_73,Z_74)),Z_73) = inverse(Z_74) ),
    inference(superposition,[status(thm),theory(equality)],[c_258,c_290]) ).

tff(c_4553,plain,
    ! [Z_18,Z_20] : ( multiply(inverse(inverse(Z_18)),inverse(multiply(Z_20,Z_18))) = inverse(Z_20) ),
    inference(superposition,[status(thm),theory(equality)],[c_336,c_4430]) ).

tff(c_4673,plain,
    ! [Z_18,Z_20] : ( multiply(Z_18,inverse(multiply(Z_20,Z_18))) = inverse(Z_20) ),
    inference(demodulation,[status(thm),theory(equality)],[c_621,c_4553]) ).

tff(c_692,plain,
    ! [Z_20,Z_18] : ( multiply(Z_20,Z_18) = multiply(Z_18,Z_20) ),
    inference(superposition,[status(thm),theory(equality)],[c_258,c_599]) ).

tff(c_541,plain,
    ! [Z_26,X_1,Y_2] : ( multiply(inverse(Z_26),Z_26) = multiply(X_1,multiply(inverse(multiply(X_1,Y_2)),Y_2)) ),
    inference(superposition,[status(thm),theory(equality)],[c_457,c_2]) ).

tff(c_5067,plain,
    ! [Z_26,X_1,Y_2] : ( multiply(inverse(Z_26),Z_26) = multiply(X_1,multiply(Y_2,inverse(multiply(X_1,Y_2)))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_692,c_541]) ).

tff(c_8222,plain,
    ! [Z_97,X_98] : ( multiply(inverse(Z_97),Z_97) = multiply(X_98,inverse(X_98)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4673,c_5067]) ).

tff(c_9103,plain,
    ! [Z_102,X_103] : ( multiply(Z_102,inverse(Z_102)) = multiply(X_103,inverse(X_103)) ),
    inference(superposition,[status(thm),theory(equality)],[c_621,c_8222]) ).

tff(c_4,plain,
    ( ( multiply(b4,a4) != multiply(a4,b4) )
    | ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
    | ( multiply(multiply(inverse(b2),b2),a2) != a2 )
    | ( multiply(inverse(b1),b1) != multiply(inverse(a1),a1) ) ),
    inference(cnfTransformation,[status(thm)],[f_36]) ).

tff(c_234,plain,
    ( ( multiply(b4,a4) != multiply(a4,b4) )
    | ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
    | ( multiply(inverse(b1),b1) != multiply(inverse(a1),a1) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_129,c_4]) ).

tff(c_235,plain,
    multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
    inference(splitLeft,[status(thm)],[c_234]) ).

tff(c_768,plain,
    multiply(b1,inverse(b1)) != multiply(a1,inverse(a1)),
    inference(demodulation,[status(thm),theory(equality)],[c_692,c_692,c_235]) ).

tff(c_9113,plain,
    ! [Z_102] : ( multiply(a1,inverse(a1)) != multiply(Z_102,inverse(Z_102)) ),
    inference(superposition,[status(thm),theory(equality)],[c_9103,c_768]) ).

tff(c_18551,plain,
    $false,
    inference(reflexivity,[status(thm),theory(equality)],[c_9113]) ).

tff(c_18552,plain,
    ( ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
    | ( multiply(b4,a4) != multiply(a4,b4) ) ),
    inference(splitRight,[status(thm)],[c_234]) ).

tff(c_234612,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_19303,c_19303,c_18861,c_19303,c_18552]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : GRP087-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.00/0.14  % 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
% 0.15/0.35  % Computer : n009.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu Aug  3 21:53:23 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 139.24/113.89  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 139.36/113.90  
% 139.36/113.90  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 139.36/113.94  
% 139.36/113.94  Inference rules
% 139.36/113.94  ----------------------
% 139.36/113.94  #Ref     : 1
% 139.36/113.94  #Sup     : 58242
% 139.36/113.94  #Fact    : 0
% 139.36/113.94  #Define  : 0
% 139.36/113.94  #Split   : 1
% 139.36/113.94  #Chain   : 0
% 139.36/113.94  #Close   : 0
% 139.36/113.94  
% 139.36/113.94  Ordering : KBO
% 139.36/113.94  
% 139.36/113.94  Simplification rules
% 139.36/113.94  ----------------------
% 139.36/113.94  #Subsume      : 5165
% 139.36/113.94  #Demod        : 114517
% 139.36/113.94  #Tautology    : 12008
% 139.36/113.94  #SimpNegUnit  : 0
% 139.36/113.94  #BackRed      : 51
% 139.36/113.94  
% 139.36/113.94  #Partial instantiations: 0
% 139.36/113.94  #Strategies tried      : 1
% 139.36/113.94  
% 139.36/113.94  Timing (in seconds)
% 139.36/113.94  ----------------------
% 139.36/113.94  Preprocessing        : 0.40
% 139.36/113.94  Parsing              : 0.21
% 139.36/113.94  CNF conversion       : 0.02
% 139.36/113.94  Main loop            : 112.49
% 139.36/113.94  Inferencing          : 6.55
% 139.36/113.94  Reduction            : 97.62
% 139.36/113.94  Demodulation         : 96.31
% 139.36/113.94  BG Simplification    : 1.22
% 139.36/113.94  Subsumption          : 4.96
% 139.36/113.94  Abstraction          : 2.38
% 139.36/113.94  MUC search           : 0.00
% 139.36/113.94  Cooper               : 0.00
% 139.36/113.94  Total                : 112.94
% 139.36/113.94  Index Insertion      : 0.00
% 139.36/113.94  Index Deletion       : 0.00
% 139.36/113.94  Index Matching       : 0.00
% 139.36/113.94  BG Taut test         : 0.00
%------------------------------------------------------------------------------