TSTP Solution File: GRP075-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP075-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 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 : n022.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 10:39:47 EDT 2023

% Result   : Unsatisfiable 7.00s 2.83s
% Output   : CNFRefutation 7.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   80 (  67 unt;   9 typ;   0 def)
%            Number of atoms       :   78 (  76 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   20 (  13   ~;   7   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :  112 (; 112   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ multiply > double_divide > #nlpp > inverse > identity > c3 > b3 > 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(inverse,type,
    inverse: $i > $i ).

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

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

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

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

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

tff(f_30,axiom,
    ! [X,Y] : ( multiply(X,Y) = double_divide(double_divide(Y,X),identity) ),
    file(unknown,unknown) ).

tff(f_33,axiom,
    ! [X] : ( inverse(X) = double_divide(X,identity) ),
    file(unknown,unknown) ).

tff(f_36,axiom,
    ! [X] : ( identity = double_divide(X,inverse(X)) ),
    file(unknown,unknown) ).

tff(f_44,axiom,
    ( ( multiply(inverse(a1),a1) != identity )
    | ( multiply(identity,a2) != a2 )
    | ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ) ),
    file(unknown,unknown) ).

tff(f_27,axiom,
    ! [X,Y,Z,U] : ( double_divide(double_divide(double_divide(X,double_divide(Y,identity)),double_divide(double_divide(Z,double_divide(U,double_divide(U,identity))),double_divide(X,identity))),Y) = Z ),
    file(unknown,unknown) ).

tff(c_28,plain,
    ! [Y_11,X_12] : ( double_divide(double_divide(Y_11,X_12),identity) = multiply(X_12,Y_11) ),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_6,plain,
    ! [X_7] : ( double_divide(X_7,identity) = inverse(X_7) ),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_37,plain,
    ! [Y_11,X_12] : ( inverse(double_divide(Y_11,X_12)) = multiply(X_12,Y_11) ),
    inference(superposition,[status(thm),theory(equality)],[c_28,c_6]) ).

tff(c_8,plain,
    ! [X_8] : ( double_divide(X_8,inverse(X_8)) = identity ),
    inference(cnfTransformation,[status(thm)],[f_36]) ).

tff(c_52,plain,
    ! [X_8] : ( multiply(inverse(X_8),X_8) = double_divide(identity,identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_28]) ).

tff(c_57,plain,
    ! [X_8] : ( multiply(inverse(X_8),X_8) = inverse(identity) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_52]) ).

tff(c_10,plain,
    ( ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
    | ( multiply(identity,a2) != a2 )
    | ( multiply(inverse(a1),a1) != identity ) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_215,plain,
    ( ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
    | ( multiply(identity,a2) != a2 )
    | ( inverse(identity) != identity ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_57,c_10]) ).

tff(c_216,plain,
    inverse(identity) != identity,
    inference(splitLeft,[status(thm)],[c_215]) ).

tff(c_2,plain,
    ! [X_1,Y_2,Z_3,U_4] : ( double_divide(double_divide(double_divide(X_1,double_divide(Y_2,identity)),double_divide(double_divide(Z_3,double_divide(U_4,double_divide(U_4,identity))),double_divide(X_1,identity))),Y_2) = Z_3 ),
    inference(cnfTransformation,[status(thm)],[f_27]) ).

tff(c_90,plain,
    ! [X_16,Y_17,Z_18] : ( double_divide(double_divide(double_divide(X_16,inverse(Y_17)),double_divide(inverse(Z_18),inverse(X_16))),Y_17) = Z_18 ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_6,c_8,c_6,c_6,c_2]) ).

tff(c_142,plain,
    ! [Z_18,Y_17] : ( double_divide(double_divide(double_divide(inverse(Z_18),inverse(Y_17)),identity),Y_17) = Z_18 ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_90]) ).

tff(c_237,plain,
    ! [Y_22,Z_23] : ( double_divide(multiply(inverse(Y_22),inverse(Z_23)),Y_22) = Z_23 ),
    inference(demodulation,[status(thm),theory(equality)],[c_37,c_6,c_142]) ).

tff(c_282,plain,
    ! [Z_24] : ( double_divide(inverse(identity),inverse(Z_24)) = Z_24 ),
    inference(superposition,[status(thm),theory(equality)],[c_57,c_237]) ).

tff(c_301,plain,
    inverse(identity) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_282,c_8]) ).

tff(c_319,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_216,c_301]) ).

tff(c_321,plain,
    inverse(identity) = identity,
    inference(splitRight,[status(thm)],[c_215]) ).

tff(c_443,plain,
    ! [Y_28,Z_29] : ( double_divide(multiply(inverse(Y_28),inverse(Z_29)),Y_28) = Z_29 ),
    inference(demodulation,[status(thm),theory(equality)],[c_37,c_6,c_142]) ).

tff(c_489,plain,
    ! [Z_29] : ( inverse(multiply(inverse(identity),inverse(Z_29))) = Z_29 ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_443]) ).

tff(c_495,plain,
    ! [Z_29] : ( inverse(multiply(identity,inverse(Z_29))) = Z_29 ),
    inference(demodulation,[status(thm),theory(equality)],[c_321,c_489]) ).

tff(c_322,plain,
    ! [X_8] : ( multiply(inverse(X_8),X_8) = identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_321,c_57]) ).

tff(c_541,plain,
    ! [Z_32] : ( double_divide(identity,inverse(Z_32)) = Z_32 ),
    inference(superposition,[status(thm),theory(equality)],[c_322,c_443]) ).

tff(c_694,plain,
    ! [Z_35] : ( multiply(inverse(Z_35),identity) = inverse(Z_35) ),
    inference(superposition,[status(thm),theory(equality)],[c_541,c_37]) ).

tff(c_707,plain,
    ! [Z_29] : ( inverse(multiply(identity,inverse(Z_29))) = multiply(Z_29,identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_495,c_694]) ).

tff(c_724,plain,
    ! [Z_29] : ( multiply(Z_29,identity) = Z_29 ),
    inference(demodulation,[status(thm),theory(equality)],[c_495,c_707]) ).

tff(c_473,plain,
    ! [Y_28] : ( double_divide(multiply(inverse(Y_28),identity),Y_28) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_321,c_443]) ).

tff(c_813,plain,
    ! [Y_38] : ( double_divide(inverse(Y_38),Y_38) = identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_724,c_473]) ).

tff(c_833,plain,
    ! [Y_38] : ( multiply(Y_38,inverse(Y_38)) = inverse(identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_813,c_37]) ).

tff(c_876,plain,
    ! [Y_39] : ( multiply(Y_39,inverse(Y_39)) = identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_321,c_833]) ).

tff(c_148,plain,
    ! [Y_17,Z_18] : ( double_divide(multiply(inverse(Y_17),inverse(Z_18)),Y_17) = Z_18 ),
    inference(demodulation,[status(thm),theory(equality)],[c_37,c_6,c_142]) ).

tff(c_926,plain,
    ! [Y_40] : ( double_divide(identity,Y_40) = inverse(Y_40) ),
    inference(superposition,[status(thm),theory(equality)],[c_876,c_148]) ).

tff(c_945,plain,
    ! [Y_40] : ( inverse(inverse(Y_40)) = multiply(Y_40,identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_926,c_37]) ).

tff(c_978,plain,
    ! [Y_40] : ( inverse(inverse(Y_40)) = Y_40 ),
    inference(demodulation,[status(thm),theory(equality)],[c_724,c_945]) ).

tff(c_65,plain,
    ! [Y_14,X_15] : ( inverse(double_divide(Y_14,X_15)) = multiply(X_15,Y_14) ),
    inference(superposition,[status(thm),theory(equality)],[c_28,c_6]) ).

tff(c_83,plain,
    ! [X_7] : ( inverse(inverse(X_7)) = multiply(identity,X_7) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_65]) ).

tff(c_1078,plain,
    ! [X_7] : ( multiply(identity,X_7) = X_7 ),
    inference(demodulation,[status(thm),theory(equality)],[c_978,c_83]) ).

tff(c_4,plain,
    ! [Y_6,X_5] : ( double_divide(double_divide(Y_6,X_5),identity) = multiply(X_5,Y_6) ),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_80,plain,
    ! [Y_6,X_5] : ( multiply(identity,double_divide(Y_6,X_5)) = inverse(multiply(X_5,Y_6)) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_65]) ).

tff(c_1326,plain,
    ! [X_5,Y_6] : ( inverse(multiply(X_5,Y_6)) = double_divide(Y_6,X_5) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1078,c_80]) ).

tff(c_11,plain,
    ! [X_1,Y_2,Z_3] : ( double_divide(double_divide(double_divide(X_1,inverse(Y_2)),double_divide(inverse(Z_3),inverse(X_1))),Y_2) = Z_3 ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_6,c_8,c_6,c_6,c_2]) ).

tff(c_830,plain,
    ! [X_1,Y_2] : ( double_divide(double_divide(double_divide(X_1,inverse(Y_2)),identity),Y_2) = inverse(X_1) ),
    inference(superposition,[status(thm),theory(equality)],[c_813,c_11]) ).

tff(c_2949,plain,
    ! [Y_83,X_84] : ( double_divide(multiply(inverse(Y_83),X_84),Y_83) = inverse(X_84) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_830]) ).

tff(c_3244,plain,
    ! [Y_87,X_88] : ( double_divide(multiply(Y_87,X_88),inverse(Y_87)) = inverse(X_88) ),
    inference(superposition,[status(thm),theory(equality)],[c_978,c_2949]) ).

tff(c_131,plain,
    ! [Z_18,X_16] : ( multiply(double_divide(inverse(Z_18),inverse(X_16)),double_divide(X_16,inverse(identity))) = Z_18 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_90]) ).

tff(c_1267,plain,
    ! [Z_46,X_47] : ( multiply(double_divide(inverse(Z_46),inverse(X_47)),inverse(X_47)) = Z_46 ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_321,c_131]) ).

tff(c_1285,plain,
    ! [Z_46,Y_40] : ( multiply(double_divide(inverse(Z_46),inverse(inverse(Y_40))),Y_40) = Z_46 ),
    inference(superposition,[status(thm),theory(equality)],[c_978,c_1267]) ).

tff(c_1500,plain,
    ! [Z_52,Y_53] : ( multiply(double_divide(inverse(Z_52),Y_53),Y_53) = Z_52 ),
    inference(demodulation,[status(thm),theory(equality)],[c_978,c_1285]) ).

tff(c_1528,plain,
    ! [Y_40,Y_53] : ( multiply(double_divide(Y_40,Y_53),Y_53) = inverse(Y_40) ),
    inference(superposition,[status(thm),theory(equality)],[c_978,c_1500]) ).

tff(c_3274,plain,
    ! [X_88,Y_87] : ( multiply(inverse(X_88),inverse(Y_87)) = inverse(multiply(Y_87,X_88)) ),
    inference(superposition,[status(thm),theory(equality)],[c_3244,c_1528]) ).

tff(c_4632,plain,
    ! [X_107,Y_108] : ( multiply(inverse(X_107),inverse(Y_108)) = double_divide(X_107,Y_108) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1326,c_3274]) ).

tff(c_4671,plain,
    ! [Y_108,X_107] : ( double_divide(inverse(Y_108),inverse(X_107)) = inverse(double_divide(X_107,Y_108)) ),
    inference(superposition,[status(thm),theory(equality)],[c_4632,c_1326]) ).

tff(c_4735,plain,
    ! [Y_108,X_107] : ( double_divide(inverse(Y_108),inverse(X_107)) = multiply(Y_108,X_107) ),
    inference(demodulation,[status(thm),theory(equality)],[c_37,c_4671]) ).

tff(c_1315,plain,
    ! [Z_46,Y_40] : ( multiply(double_divide(inverse(Z_46),Y_40),Y_40) = Z_46 ),
    inference(demodulation,[status(thm),theory(equality)],[c_978,c_1285]) ).

tff(c_3325,plain,
    ! [Z_46,Y_40] : ( double_divide(Z_46,inverse(double_divide(inverse(Z_46),Y_40))) = inverse(Y_40) ),
    inference(superposition,[status(thm),theory(equality)],[c_1315,c_3244]) ).

tff(c_3938,plain,
    ! [Z_97,Y_98] : ( double_divide(Z_97,multiply(Y_98,inverse(Z_97))) = inverse(Y_98) ),
    inference(demodulation,[status(thm),theory(equality)],[c_37,c_3325]) ).

tff(c_4028,plain,
    ! [Y_40,Y_98] : ( double_divide(inverse(Y_40),multiply(Y_98,Y_40)) = inverse(Y_98) ),
    inference(superposition,[status(thm),theory(equality)],[c_978,c_3938]) ).

tff(c_450,plain,
    ! [Z_29,Z_3,Y_2] : ( double_divide(double_divide(Z_29,double_divide(inverse(Z_3),inverse(multiply(inverse(inverse(Y_2)),inverse(Z_29))))),Y_2) = Z_3 ),
    inference(superposition,[status(thm),theory(equality)],[c_443,c_11]) ).

tff(c_491,plain,
    ! [Z_29,Z_3,Y_2] : ( double_divide(double_divide(Z_29,double_divide(inverse(Z_3),inverse(multiply(multiply(identity,Y_2),inverse(Z_29))))),Y_2) = Z_3 ),
    inference(demodulation,[status(thm),theory(equality)],[c_83,c_450]) ).

tff(c_6796,plain,
    ! [Z_137,Z_138,Y_139] : ( double_divide(double_divide(Z_137,double_divide(inverse(Z_138),double_divide(inverse(Z_137),Y_139))),Y_139) = Z_138 ),
    inference(demodulation,[status(thm),theory(equality)],[c_1326,c_1078,c_491]) ).

tff(c_6903,plain,
    ! [Y_40,Z_138,Y_98] : ( double_divide(double_divide(Y_40,double_divide(inverse(Z_138),inverse(Y_98))),multiply(Y_98,Y_40)) = Z_138 ),
    inference(superposition,[status(thm),theory(equality)],[c_4028,c_6796]) ).

tff(c_7496,plain,
    ! [Y_147,Z_148,Y_149] : ( double_divide(double_divide(Y_147,multiply(Z_148,Y_149)),multiply(Y_149,Y_147)) = Z_148 ),
    inference(demodulation,[status(thm),theory(equality)],[c_4735,c_6903]) ).

tff(c_1522,plain,
    ! [Y_6,X_5,Y_53] : ( multiply(double_divide(double_divide(Y_6,X_5),Y_53),Y_53) = multiply(X_5,Y_6) ),
    inference(superposition,[status(thm),theory(equality)],[c_1326,c_1500]) ).

tff(c_7511,plain,
    ! [Z_148,Y_149,Y_147] : ( multiply(multiply(Z_148,Y_149),Y_147) = multiply(Z_148,multiply(Y_149,Y_147)) ),
    inference(superposition,[status(thm),theory(equality)],[c_7496,c_1522]) ).

tff(c_320,plain,
    ( ( multiply(identity,a2) != a2 )
    | ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ) ),
    inference(splitRight,[status(thm)],[c_215]) ).

tff(c_2731,plain,
    multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
    inference(demodulation,[status(thm),theory(equality)],[c_1078,c_320]) ).

tff(c_10833,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_7511,c_2731]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRP075-1 : TPTP v8.1.2. Bugfixed v2.3.0.
% 0.00/0.13  % 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
% 0.14/0.34  % Computer : n022.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 22:11:03 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 7.00/2.83  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.36/2.84  
% 7.36/2.84  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.36/2.87  
% 7.36/2.87  Inference rules
% 7.36/2.87  ----------------------
% 7.36/2.87  #Ref     : 0
% 7.36/2.87  #Sup     : 2682
% 7.36/2.87  #Fact    : 0
% 7.36/2.87  #Define  : 0
% 7.36/2.87  #Split   : 1
% 7.36/2.87  #Chain   : 0
% 7.36/2.87  #Close   : 0
% 7.36/2.87  
% 7.36/2.87  Ordering : KBO
% 7.36/2.87  
% 7.36/2.87  Simplification rules
% 7.36/2.87  ----------------------
% 7.36/2.87  #Subsume      : 0
% 7.36/2.87  #Demod        : 4203
% 7.36/2.87  #Tautology    : 1754
% 7.36/2.87  #SimpNegUnit  : 1
% 7.36/2.87  #BackRed      : 25
% 7.36/2.87  
% 7.36/2.87  #Partial instantiations: 0
% 7.36/2.87  #Strategies tried      : 1
% 7.36/2.87  
% 7.36/2.87  Timing (in seconds)
% 7.36/2.87  ----------------------
% 7.36/2.88  Preprocessing        : 0.43
% 7.36/2.88  Parsing              : 0.23
% 7.36/2.88  CNF conversion       : 0.02
% 7.36/2.88  Main loop            : 1.38
% 7.36/2.88  Inferencing          : 0.46
% 7.36/2.88  Reduction            : 0.60
% 7.36/2.88  Demodulation         : 0.51
% 7.36/2.88  BG Simplification    : 0.05
% 7.36/2.88  Subsumption          : 0.18
% 7.36/2.88  Abstraction          : 0.08
% 7.36/2.88  MUC search           : 0.00
% 7.36/2.88  Cooper               : 0.00
% 7.36/2.88  Total                : 1.86
% 7.36/2.88  Index Insertion      : 0.00
% 7.36/2.88  Index Deletion       : 0.00
% 7.36/2.88  Index Matching       : 0.00
% 7.36/2.88  BG Taut test         : 0.00
%------------------------------------------------------------------------------