TSTP Solution File: GRP039-5 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP039-5 : TPTP v8.1.2. Released v1.0.0.
% 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 : n012.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 10:39:42 EDT 2023

% Result   : Unsatisfiable 6.38s 2.54s
% Output   : CNFRefutation 6.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   70 (  39 unt;   9 typ;   0 def)
%            Number of atoms       :   98 (  36 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   63 (  26   ~;  37   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   4   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   48 (;  48   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subgroup_member > multiply > element_in_O2 > #nlpp > inverse > identity > d > c > b > a

%Foreground sorts:

%Background operators:

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

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

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

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

tff(element_in_O2,type,
    element_in_O2: ( $i * $i ) > $i ).

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

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

tff(subgroup_member,type,
    subgroup_member: $i > $o ).

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

tff(f_146,axiom,
    ~ subgroup_member(d),
    file(unknown,unknown) ).

tff(f_144,axiom,
    multiply(a,c) = d,
    file(unknown,unknown) ).

tff(f_118,axiom,
    ! [X,Y,Z] :
      ( ~ subgroup_member(X)
      | ~ subgroup_member(Y)
      | ( multiply(X,Y) != Z )
      | subgroup_member(Z) ),
    file(unknown,unknown) ).

tff(f_142,axiom,
    subgroup_member(b),
    file(unknown,unknown) ).

tff(f_123,axiom,
    ! [X] : ( multiply(X,identity) = X ),
    file(unknown,unknown) ).

tff(f_73,axiom,
    ! [X] : ( multiply(inverse(X),X) = identity ),
    file(unknown,unknown) ).

tff(f_143,axiom,
    multiply(b,inverse(a)) = c,
    file(unknown,unknown) ).

tff(f_76,axiom,
    ! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
    file(unknown,unknown) ).

tff(f_69,axiom,
    ! [X] : ( multiply(identity,X) = X ),
    file(unknown,unknown) ).

tff(f_140,axiom,
    ! [X,Y] :
      ( subgroup_member(X)
      | subgroup_member(Y)
      | ( multiply(X,element_in_O2(X,Y)) = Y ) ),
    file(unknown,unknown) ).

tff(f_125,axiom,
    ! [X] : ( multiply(X,inverse(X)) = identity ),
    file(unknown,unknown) ).

tff(f_134,axiom,
    ! [X,Y] :
      ( subgroup_member(X)
      | subgroup_member(Y)
      | subgroup_member(element_in_O2(X,Y)) ),
    file(unknown,unknown) ).

tff(f_107,axiom,
    ! [X] :
      ( ~ subgroup_member(X)
      | subgroup_member(inverse(X)) ),
    file(unknown,unknown) ).

tff(c_28,plain,
    ~ subgroup_member(d),
    inference(cnfTransformation,[status(thm)],[f_146]) ).

tff(c_26,plain,
    multiply(a,c) = d,
    inference(cnfTransformation,[status(thm)],[f_144]) ).

tff(c_117,plain,
    ! [X_23,Y_24] :
      ( subgroup_member(multiply(X_23,Y_24))
      | ~ subgroup_member(Y_24)
      | ~ subgroup_member(X_23) ),
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_135,plain,
    ( subgroup_member(d)
    | ~ subgroup_member(c)
    | ~ subgroup_member(a) ),
    inference(superposition,[status(thm),theory(equality)],[c_26,c_117]) ).

tff(c_144,plain,
    ( ~ subgroup_member(c)
    | ~ subgroup_member(a) ),
    inference(negUnitSimplification,[status(thm)],[c_28,c_135]) ).

tff(c_145,plain,
    ~ subgroup_member(a),
    inference(splitLeft,[status(thm)],[c_144]) ).

tff(c_22,plain,
    subgroup_member(b),
    inference(cnfTransformation,[status(thm)],[f_142]) ).

tff(c_12,plain,
    ! [X_10] : ( multiply(X_10,identity) = X_10 ),
    inference(cnfTransformation,[status(thm)],[f_123]) ).

tff(c_4,plain,
    ! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_24,plain,
    multiply(b,inverse(a)) = c,
    inference(cnfTransformation,[status(thm)],[f_143]) ).

tff(c_146,plain,
    ! [X_25,Y_26,Z_27] : ( multiply(multiply(X_25,Y_26),Z_27) = multiply(X_25,multiply(Y_26,Z_27)) ),
    inference(cnfTransformation,[status(thm)],[f_76]) ).

tff(c_599,plain,
    ! [Z_38] : ( multiply(b,multiply(inverse(a),Z_38)) = multiply(c,Z_38) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_146]) ).

tff(c_633,plain,
    multiply(c,a) = multiply(b,identity),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_599]) ).

tff(c_649,plain,
    multiply(c,a) = b,
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_633]) ).

tff(c_2,plain,
    ! [X_1] : ( multiply(identity,X_1) = X_1 ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_175,plain,
    ! [X_2,Z_27] : ( multiply(inverse(X_2),multiply(X_2,Z_27)) = multiply(identity,Z_27) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_146]) ).

tff(c_201,plain,
    ! [X_2,Z_27] : ( multiply(inverse(X_2),multiply(X_2,Z_27)) = Z_27 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_175]) ).

tff(c_658,plain,
    multiply(inverse(c),b) = a,
    inference(superposition,[status(thm),theory(equality)],[c_649,c_201]) ).

tff(c_10,plain,
    ! [X_7,Y_8] :
      ( subgroup_member(multiply(X_7,Y_8))
      | ~ subgroup_member(Y_8)
      | ~ subgroup_member(X_7) ),
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_682,plain,
    ( subgroup_member(a)
    | ~ subgroup_member(b)
    | ~ subgroup_member(inverse(c)) ),
    inference(superposition,[status(thm),theory(equality)],[c_658,c_10]) ).

tff(c_688,plain,
    ( subgroup_member(a)
    | ~ subgroup_member(inverse(c)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_682]) ).

tff(c_689,plain,
    ~ subgroup_member(inverse(c)),
    inference(negUnitSimplification,[status(thm)],[c_145,c_688]) ).

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_76]) ).

tff(c_211,plain,
    ! [X_28,Y_29] :
      ( ( multiply(X_28,element_in_O2(X_28,Y_29)) = Y_29 )
      | subgroup_member(Y_29)
      | subgroup_member(X_28) ),
    inference(cnfTransformation,[status(thm)],[f_140]) ).

tff(c_3051,plain,
    ! [X_67,Y_68,Y_69] :
      ( ( multiply(X_67,multiply(Y_68,element_in_O2(multiply(X_67,Y_68),Y_69))) = Y_69 )
      | subgroup_member(Y_69)
      | subgroup_member(multiply(X_67,Y_68)) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_211]) ).

tff(c_195,plain,
    ! [Z_27] : ( multiply(a,multiply(c,Z_27)) = multiply(d,Z_27) ),
    inference(superposition,[status(thm),theory(equality)],[c_26,c_146]) ).

tff(c_3131,plain,
    ! [Y_69] :
      ( ( multiply(d,element_in_O2(multiply(a,c),Y_69)) = Y_69 )
      | subgroup_member(Y_69)
      | subgroup_member(multiply(a,c)) ),
    inference(superposition,[status(thm),theory(equality)],[c_3051,c_195]) ).

tff(c_3337,plain,
    ! [Y_69] :
      ( ( multiply(d,element_in_O2(d,Y_69)) = Y_69 )
      | subgroup_member(Y_69)
      | subgroup_member(d) ),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_26,c_3131]) ).

tff(c_3412,plain,
    ! [Y_70] :
      ( ( multiply(d,element_in_O2(d,Y_70)) = Y_70 )
      | subgroup_member(Y_70) ),
    inference(negUnitSimplification,[status(thm)],[c_28,c_3337]) ).

tff(c_5271,plain,
    ! [Y_95] :
      ( ( multiply(inverse(d),Y_95) = element_in_O2(d,Y_95) )
      | subgroup_member(Y_95) ),
    inference(superposition,[status(thm),theory(equality)],[c_3412,c_201]) ).

tff(c_14,plain,
    ! [X_11] : ( multiply(X_11,inverse(X_11)) = identity ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_442,plain,
    ! [Z_36] : ( multiply(a,multiply(c,Z_36)) = multiply(d,Z_36) ),
    inference(superposition,[status(thm),theory(equality)],[c_26,c_146]) ).

tff(c_469,plain,
    multiply(d,inverse(c)) = multiply(a,identity),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_442]) ).

tff(c_477,plain,
    multiply(d,inverse(c)) = a,
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_469]) ).

tff(c_482,plain,
    multiply(inverse(d),a) = inverse(c),
    inference(superposition,[status(thm),theory(equality)],[c_477,c_201]) ).

tff(c_5367,plain,
    ( ( element_in_O2(d,a) = inverse(c) )
    | subgroup_member(a) ),
    inference(superposition,[status(thm),theory(equality)],[c_5271,c_482]) ).

tff(c_5473,plain,
    element_in_O2(d,a) = inverse(c),
    inference(negUnitSimplification,[status(thm)],[c_145,c_5367]) ).

tff(c_18,plain,
    ! [X_12,Y_13] :
      ( subgroup_member(element_in_O2(X_12,Y_13))
      | subgroup_member(Y_13)
      | subgroup_member(X_12) ),
    inference(cnfTransformation,[status(thm)],[f_134]) ).

tff(c_5532,plain,
    ( subgroup_member(inverse(c))
    | subgroup_member(a)
    | subgroup_member(d) ),
    inference(superposition,[status(thm),theory(equality)],[c_5473,c_18]) ).

tff(c_5542,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_28,c_145,c_689,c_5532]) ).

tff(c_5544,plain,
    subgroup_member(a),
    inference(splitRight,[status(thm)],[c_144]) ).

tff(c_8,plain,
    ! [X_6] :
      ( subgroup_member(inverse(X_6))
      | ~ subgroup_member(X_6) ),
    inference(cnfTransformation,[status(thm)],[f_107]) ).

tff(c_5543,plain,
    ~ subgroup_member(c),
    inference(splitRight,[status(thm)],[c_144]) ).

tff(c_120,plain,
    ( subgroup_member(c)
    | ~ subgroup_member(inverse(a))
    | ~ subgroup_member(b) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_117]) ).

tff(c_137,plain,
    ( subgroup_member(c)
    | ~ subgroup_member(inverse(a)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_120]) ).

tff(c_5605,plain,
    ~ subgroup_member(inverse(a)),
    inference(negUnitSimplification,[status(thm)],[c_5543,c_137]) ).

tff(c_5608,plain,
    ~ subgroup_member(a),
    inference(resolution,[status(thm)],[c_8,c_5605]) ).

tff(c_5612,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_5544,c_5608]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : GRP039-5 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14  % 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
% 0.14/0.35  % Computer : n012.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 22:06:52 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 6.38/2.54  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.38/2.56  
% 6.38/2.56  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.38/2.60  
% 6.38/2.60  Inference rules
% 6.38/2.60  ----------------------
% 6.38/2.60  #Ref     : 0
% 6.38/2.60  #Sup     : 1358
% 6.38/2.60  #Fact    : 0
% 6.38/2.60  #Define  : 0
% 6.38/2.60  #Split   : 4
% 6.38/2.60  #Chain   : 0
% 6.38/2.60  #Close   : 0
% 6.38/2.60  
% 6.38/2.60  Ordering : KBO
% 6.38/2.60  
% 6.38/2.60  Simplification rules
% 6.38/2.60  ----------------------
% 6.38/2.60  #Subsume      : 261
% 6.38/2.60  #Demod        : 1239
% 6.38/2.60  #Tautology    : 651
% 6.38/2.60  #SimpNegUnit  : 162
% 6.38/2.60  #BackRed      : 7
% 6.38/2.60  
% 6.38/2.60  #Partial instantiations: 0
% 6.38/2.60  #Strategies tried      : 1
% 6.38/2.60  
% 6.38/2.60  Timing (in seconds)
% 6.38/2.60  ----------------------
% 6.38/2.60  Preprocessing        : 0.47
% 6.38/2.60  Parsing              : 0.23
% 6.38/2.60  CNF conversion       : 0.02
% 6.38/2.60  Main loop            : 1.03
% 6.38/2.60  Inferencing          : 0.36
% 6.38/2.60  Reduction            : 0.39
% 6.38/2.60  Demodulation         : 0.30
% 6.38/2.60  BG Simplification    : 0.04
% 6.38/2.60  Subsumption          : 0.16
% 6.38/2.60  Abstraction          : 0.04
% 6.38/2.60  MUC search           : 0.00
% 6.38/2.60  Cooper               : 0.00
% 6.38/2.60  Total                : 1.56
% 6.38/2.60  Index Insertion      : 0.00
% 6.38/2.60  Index Deletion       : 0.00
% 6.38/2.60  Index Matching       : 0.00
% 6.38/2.60  BG Taut test         : 0.00
%------------------------------------------------------------------------------