TSTP Solution File: GRP576-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP576-1 : 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 : n017.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 10:41:33 EDT 2023

% Result   : Unsatisfiable 4.29s 2.29s
% Output   : CNFRefutation 5.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   78 (  72 unt;   6 typ;   0 def)
%            Number of atoms       :   72 (  71 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    :    6 (   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    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  107 (; 107   !;   0   ?;   0   :)

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

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

tff(f_28,axiom,
    ! [A] : ( inverse(A) = double_divide(A,identity) ),
    file(unknown,unknown) ).

tff(f_30,axiom,
    ! [A] : ( identity = double_divide(A,inverse(A)) ),
    file(unknown,unknown) ).

tff(f_24,axiom,
    ! [A,B,C] : ( double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B ),
    file(unknown,unknown) ).

tff(f_26,axiom,
    ! [A,B] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
    file(unknown,unknown) ).

tff(f_32,axiom,
    multiply(a,b) != multiply(b,a),
    file(unknown,unknown) ).

tff(c_6,plain,
    ! [A_6] : ( double_divide(A_6,identity) = inverse(A_6) ),
    inference(cnfTransformation,[status(thm)],[f_28]) ).

tff(c_8,plain,
    ! [A_7] : ( double_divide(A_7,inverse(A_7)) = identity ),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_2,plain,
    ! [A_1,B_2,C_3] : ( double_divide(double_divide(A_1,double_divide(double_divide(B_2,double_divide(C_3,A_1)),double_divide(C_3,identity))),double_divide(identity,identity)) = B_2 ),
    inference(cnfTransformation,[status(thm)],[f_24]) ).

tff(c_65,plain,
    ! [A_13,B_14,C_15] : ( double_divide(double_divide(A_13,double_divide(double_divide(B_14,double_divide(C_15,A_13)),inverse(C_15))),inverse(identity)) = B_14 ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_6,c_2]) ).

tff(c_553,plain,
    ! [B_33,A_34] : ( double_divide(double_divide(identity,double_divide(double_divide(B_33,inverse(A_34)),inverse(A_34))),inverse(identity)) = B_33 ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_65]) ).

tff(c_617,plain,
    ! [A_35] : ( double_divide(double_divide(identity,double_divide(identity,inverse(A_35))),inverse(identity)) = A_35 ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_553]) ).

tff(c_657,plain,
    double_divide(double_divide(identity,identity),inverse(identity)) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_8,c_617]) ).

tff(c_662,plain,
    double_divide(inverse(identity),inverse(identity)) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_657]) ).

tff(c_86,plain,
    ! [B_14,A_6] : ( double_divide(double_divide(identity,double_divide(double_divide(B_14,inverse(A_6)),inverse(A_6))),inverse(identity)) = B_14 ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_65]) ).

tff(c_666,plain,
    double_divide(double_divide(identity,double_divide(identity,inverse(identity))),inverse(identity)) = inverse(identity),
    inference(superposition,[status(thm),theory(equality)],[c_662,c_86]) ).

tff(c_690,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_662,c_6,c_8,c_666]) ).

tff(c_28,plain,
    ! [B_10,A_11] : ( double_divide(double_divide(B_10,A_11),identity) = multiply(A_11,B_10) ),
    inference(cnfTransformation,[status(thm)],[f_26]) ).

tff(c_94,plain,
    ! [B_16,A_17] : ( inverse(double_divide(B_16,A_17)) = multiply(A_17,B_16) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_28]) ).

tff(c_118,plain,
    ! [A_6] : ( inverse(inverse(A_6)) = multiply(identity,A_6) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_94]) ).

tff(c_89,plain,
    ! [A_7,B_14] : ( double_divide(double_divide(inverse(A_7),double_divide(double_divide(B_14,identity),inverse(A_7))),inverse(identity)) = B_14 ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_65]) ).

tff(c_425,plain,
    ! [A_29,B_30] : ( double_divide(double_divide(inverse(A_29),double_divide(inverse(B_30),inverse(A_29))),inverse(identity)) = B_30 ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_89]) ).

tff(c_471,plain,
    ! [B_30] : ( double_divide(double_divide(inverse(inverse(B_30)),identity),inverse(identity)) = B_30 ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_425]) ).

tff(c_480,plain,
    ! [B_30] : ( double_divide(inverse(multiply(identity,B_30)),inverse(identity)) = B_30 ),
    inference(demodulation,[status(thm),theory(equality)],[c_118,c_6,c_471]) ).

tff(c_1038,plain,
    ! [B_45] : ( double_divide(inverse(multiply(identity,B_45)),identity) = B_45 ),
    inference(demodulation,[status(thm),theory(equality)],[c_690,c_480]) ).

tff(c_46,plain,
    ! [A_6] : ( double_divide(inverse(A_6),identity) = multiply(identity,A_6) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_28]) ).

tff(c_1053,plain,
    ! [B_45] : ( multiply(identity,multiply(identity,B_45)) = B_45 ),
    inference(superposition,[status(thm),theory(equality)],[c_1038,c_46]) ).

tff(c_153,plain,
    ! [A_19] : ( double_divide(inverse(A_19),identity) = multiply(identity,A_19) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_28]) ).

tff(c_49,plain,
    ! [B_10,A_11] : ( inverse(double_divide(B_10,A_11)) = multiply(A_11,B_10) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_28]) ).

tff(c_159,plain,
    ! [A_19] : ( multiply(identity,inverse(A_19)) = inverse(multiply(identity,A_19)) ),
    inference(superposition,[status(thm),theory(equality)],[c_153,c_49]) ).

tff(c_802,plain,
    multiply(identity,identity) = double_divide(identity,identity),
    inference(superposition,[status(thm),theory(equality)],[c_690,c_46]) ).

tff(c_811,plain,
    multiply(identity,identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_690,c_6,c_802]) ).

tff(c_11,plain,
    ! [A_1,B_2,C_3] : ( double_divide(double_divide(A_1,double_divide(double_divide(B_2,double_divide(C_3,A_1)),inverse(C_3))),inverse(identity)) = B_2 ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_6,c_2]) ).

tff(c_641,plain,
    ! [A_35] : ( double_divide(double_divide(inverse(A_35),A_35),inverse(identity)) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_617,c_11]) ).

tff(c_1823,plain,
    ! [A_59] : ( multiply(A_59,inverse(A_59)) = identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_49,c_6,c_690,c_641]) ).

tff(c_106,plain,
    ! [B_16,A_17] : ( double_divide(double_divide(B_16,A_17),multiply(A_17,B_16)) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_94,c_8]) ).

tff(c_1903,plain,
    ! [A_60] : ( double_divide(double_divide(inverse(A_60),A_60),identity) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_1823,c_106]) ).

tff(c_4,plain,
    ! [B_5,A_4] : ( double_divide(double_divide(B_5,A_4),identity) = multiply(A_4,B_5) ),
    inference(cnfTransformation,[status(thm)],[f_26]) ).

tff(c_1926,plain,
    ! [A_60] : ( multiply(identity,double_divide(inverse(A_60),A_60)) = double_divide(identity,identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_1903,c_4]) ).

tff(c_2173,plain,
    ! [A_63] : ( multiply(identity,double_divide(inverse(A_63),A_63)) = identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_690,c_6,c_1926]) ).

tff(c_1062,plain,
    ! [B_45] : ( inverse(inverse(multiply(identity,B_45))) = B_45 ),
    inference(superposition,[status(thm),theory(equality)],[c_1038,c_6]) ).

tff(c_2190,plain,
    ! [A_63] : ( double_divide(inverse(A_63),A_63) = inverse(inverse(identity)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2173,c_1062]) ).

tff(c_2269,plain,
    ! [A_64] : ( double_divide(inverse(A_64),A_64) = identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_811,c_118,c_2190]) ).

tff(c_31,plain,
    ! [B_10,A_11] : ( multiply(identity,double_divide(B_10,A_11)) = double_divide(multiply(A_11,B_10),identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_28,c_4]) ).

tff(c_53,plain,
    ! [B_10,A_11] : ( multiply(identity,double_divide(B_10,A_11)) = inverse(multiply(A_11,B_10)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_31]) ).

tff(c_446,plain,
    ! [A_29,B_30] : ( multiply(inverse(identity),double_divide(inverse(A_29),double_divide(inverse(B_30),inverse(A_29)))) = double_divide(B_30,identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_425,c_4]) ).

tff(c_474,plain,
    ! [A_29,B_30] : ( multiply(inverse(identity),double_divide(inverse(A_29),double_divide(inverse(B_30),inverse(A_29)))) = inverse(B_30) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_446]) ).

tff(c_1656,plain,
    ! [B_30,A_29] : ( inverse(multiply(double_divide(inverse(B_30),inverse(A_29)),inverse(A_29))) = inverse(B_30) ),
    inference(demodulation,[status(thm),theory(equality)],[c_53,c_690,c_474]) ).

tff(c_2275,plain,
    ! [A_29] : ( inverse(multiply(identity,inverse(A_29))) = inverse(inverse(A_29)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2269,c_1656]) ).

tff(c_2352,plain,
    ! [A_29] : ( multiply(identity,A_29) = A_29 ),
    inference(demodulation,[status(thm),theory(equality)],[c_1053,c_118,c_159,c_118,c_2275]) ).

tff(c_2376,plain,
    ! [A_11,B_10] : ( inverse(multiply(A_11,B_10)) = double_divide(B_10,A_11) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2352,c_53]) ).

tff(c_2372,plain,
    ! [B_45] : ( inverse(inverse(B_45)) = B_45 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2352,c_1062]) ).

tff(c_440,plain,
    ! [A_29,B_30] : ( multiply(inverse(identity),double_divide(inverse(A_29),double_divide(inverse(B_30),inverse(A_29)))) = inverse(B_30) ),
    inference(superposition,[status(thm),theory(equality)],[c_425,c_49]) ).

tff(c_2491,plain,
    ! [A_67,B_68] : ( double_divide(inverse(A_67),double_divide(inverse(B_68),inverse(A_67))) = inverse(B_68) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2352,c_690,c_440]) ).

tff(c_2579,plain,
    ! [B_68] : ( double_divide(inverse(identity),double_divide(inverse(B_68),identity)) = inverse(B_68) ),
    inference(superposition,[status(thm),theory(equality)],[c_690,c_2491]) ).

tff(c_2619,plain,
    ! [B_68] : ( double_divide(identity,B_68) = inverse(B_68) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2372,c_690,c_6,c_2579]) ).

tff(c_3129,plain,
    ! [A_80,B_81] : ( inverse(multiply(A_80,B_81)) = double_divide(B_81,A_80) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2352,c_53]) ).

tff(c_3221,plain,
    ! [A_82,B_83] : ( double_divide(multiply(A_82,B_83),double_divide(B_83,A_82)) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_3129,c_8]) ).

tff(c_74,plain,
    ! [A_13,B_14,C_15] : ( multiply(inverse(identity),double_divide(A_13,double_divide(double_divide(B_14,double_divide(C_15,A_13)),inverse(C_15)))) = double_divide(B_14,identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_65,c_4]) ).

tff(c_91,plain,
    ! [A_13,B_14,C_15] : ( multiply(inverse(identity),double_divide(A_13,double_divide(double_divide(B_14,double_divide(C_15,A_13)),inverse(C_15)))) = inverse(B_14) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_74]) ).

tff(c_854,plain,
    ! [B_14,C_15,A_13] : ( inverse(multiply(double_divide(double_divide(B_14,double_divide(C_15,A_13)),inverse(C_15)),A_13)) = inverse(B_14) ),
    inference(demodulation,[status(thm),theory(equality)],[c_53,c_690,c_91]) ).

tff(c_3241,plain,
    ! [B_83,A_82] : ( inverse(multiply(double_divide(identity,inverse(B_83)),A_82)) = inverse(multiply(A_82,B_83)) ),
    inference(superposition,[status(thm),theory(equality)],[c_3221,c_854]) ).

tff(c_3518,plain,
    ! [B_87,A_88] : ( double_divide(B_87,A_88) = double_divide(A_88,B_87) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2376,c_2376,c_2372,c_2619,c_3241]) ).

tff(c_4545,plain,
    ! [A_103,B_104] : ( double_divide(double_divide(A_103,B_104),identity) = multiply(A_103,B_104) ),
    inference(superposition,[status(thm),theory(equality)],[c_3518,c_4]) ).

tff(c_577,plain,
    ! [B_33,A_34] : ( multiply(inverse(identity),double_divide(identity,double_divide(double_divide(B_33,inverse(A_34)),inverse(A_34)))) = double_divide(B_33,identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_553,c_4]) ).

tff(c_610,plain,
    ! [B_33,A_34] : ( multiply(inverse(identity),double_divide(identity,double_divide(double_divide(B_33,inverse(A_34)),inverse(A_34)))) = inverse(B_33) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_577]) ).

tff(c_3059,plain,
    ! [A_78,B_79] : ( multiply(inverse(A_78),double_divide(B_79,inverse(A_78))) = inverse(B_79) ),
    inference(demodulation,[status(thm),theory(equality)],[c_49,c_2619,c_2352,c_690,c_610]) ).

tff(c_3078,plain,
    ! [B_45,B_79] : ( multiply(inverse(inverse(B_45)),double_divide(B_79,B_45)) = inverse(B_79) ),
    inference(superposition,[status(thm),theory(equality)],[c_2372,c_3059]) ).

tff(c_3108,plain,
    ! [B_45,B_79] : ( multiply(B_45,double_divide(B_79,B_45)) = inverse(B_79) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2372,c_3078]) ).

tff(c_4557,plain,
    ! [A_103,B_104] : ( multiply(identity,multiply(A_103,B_104)) = inverse(double_divide(A_103,B_104)) ),
    inference(superposition,[status(thm),theory(equality)],[c_4545,c_3108]) ).

tff(c_4688,plain,
    ! [B_104,A_103] : ( multiply(B_104,A_103) = multiply(A_103,B_104) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2352,c_49,c_4557]) ).

tff(c_10,plain,
    multiply(b,a) != multiply(a,b),
    inference(cnfTransformation,[status(thm)],[f_32]) ).

tff(c_4720,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_4688,c_10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : GRP576-1 : 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
% 0.14/0.36  % Computer : n017.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 21:29:22 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 4.29/2.29  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.29/2.30  
% 4.29/2.30  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.13/2.34  
% 5.13/2.34  Inference rules
% 5.13/2.34  ----------------------
% 5.13/2.34  #Ref     : 0
% 5.13/2.34  #Sup     : 1185
% 5.13/2.34  #Fact    : 0
% 5.13/2.34  #Define  : 0
% 5.13/2.34  #Split   : 0
% 5.13/2.34  #Chain   : 0
% 5.13/2.34  #Close   : 0
% 5.13/2.34  
% 5.13/2.34  Ordering : KBO
% 5.13/2.34  
% 5.13/2.34  Simplification rules
% 5.13/2.34  ----------------------
% 5.13/2.34  #Subsume      : 9
% 5.13/2.34  #Demod        : 1480
% 5.13/2.34  #Tautology    : 712
% 5.13/2.34  #SimpNegUnit  : 0
% 5.13/2.34  #BackRed      : 30
% 5.13/2.34  
% 5.13/2.34  #Partial instantiations: 0
% 5.13/2.34  #Strategies tried      : 1
% 5.13/2.34  
% 5.13/2.34  Timing (in seconds)
% 5.13/2.34  ----------------------
% 5.13/2.34  Preprocessing        : 0.41
% 5.13/2.34  Parsing              : 0.21
% 5.13/2.34  CNF conversion       : 0.02
% 5.13/2.34  Main loop            : 0.86
% 5.13/2.34  Inferencing          : 0.30
% 5.46/2.34  Reduction            : 0.33
% 5.46/2.34  Demodulation         : 0.27
% 5.46/2.34  BG Simplification    : 0.04
% 5.46/2.35  Subsumption          : 0.12
% 5.46/2.35  Abstraction          : 0.05
% 5.46/2.35  MUC search           : 0.00
% 5.46/2.35  Cooper               : 0.00
% 5.46/2.35  Total                : 1.33
% 5.46/2.35  Index Insertion      : 0.00
% 5.46/2.35  Index Deletion       : 0.00
% 5.46/2.35  Index Matching       : 0.00
% 5.46/2.35  BG Taut test         : 0.00
%------------------------------------------------------------------------------