TSTP Solution File: GRP039-7 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP039-7 : TPTP v8.1.2. Bugfixed v1.0.1.
% 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 : n019.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 6.28s 2.52s
% Output   : CNFRefutation 6.28s
% 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_153,axiom,
    ~ subgroup_member(d),
    file(unknown,unknown) ).

tff(f_151,axiom,
    multiply(a,c) = d,
    file(unknown,unknown) ).

tff(f_121,axiom,
    ! [X,Y,Z] :
      ( ~ subgroup_member(X)
      | ~ subgroup_member(Y)
      | ( multiply(X,Y) != Z )
      | subgroup_member(Z) ),
    file(unknown,unknown) ).

tff(f_149,axiom,
    subgroup_member(b),
    file(unknown,unknown) ).

tff(f_126,axiom,
    ! [X] : ( multiply(X,identity) = X ),
    file(unknown,unknown) ).

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

tff(f_150,axiom,
    multiply(b,inverse(a)) = c,
    file(unknown,unknown) ).

tff(f_79,axiom,
    ! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
    file(unknown,unknown) ).

tff(f_72,axiom,
    ! [X] : ( multiply(identity,X) = X ),
    file(unknown,unknown) ).

tff(f_147,axiom,
    ! [X,Y] :
      ( subgroup_member(X)
      | subgroup_member(Y)
      | ( multiply(X,element_in_O2(X,Y)) = Y ) ),
    file(unknown,unknown) ).

tff(f_128,axiom,
    ! [X] : ( multiply(X,inverse(X)) = identity ),
    file(unknown,unknown) ).

tff(f_141,axiom,
    ! [X,Y] :
      ( subgroup_member(X)
      | subgroup_member(Y)
      | subgroup_member(element_in_O2(X,Y)) ),
    file(unknown,unknown) ).

tff(f_110,axiom,
    ! [X] :
      ( ~ subgroup_member(X)
      | subgroup_member(inverse(X)) ),
    file(unknown,unknown) ).

tff(c_32,plain,
    ~ subgroup_member(d),
    inference(cnfTransformation,[status(thm)],[f_153]) ).

tff(c_30,plain,
    multiply(a,c) = d,
    inference(cnfTransformation,[status(thm)],[f_151]) ).

tff(c_166,plain,
    ! [X_24,Y_25] :
      ( subgroup_member(multiply(X_24,Y_25))
      | ~ subgroup_member(Y_25)
      | ~ subgroup_member(X_24) ),
    inference(cnfTransformation,[status(thm)],[f_121]) ).

tff(c_181,plain,
    ( subgroup_member(d)
    | ~ subgroup_member(c)
    | ~ subgroup_member(a) ),
    inference(superposition,[status(thm),theory(equality)],[c_30,c_166]) ).

tff(c_191,plain,
    ( ~ subgroup_member(c)
    | ~ subgroup_member(a) ),
    inference(negUnitSimplification,[status(thm)],[c_32,c_181]) ).

tff(c_195,plain,
    ~ subgroup_member(a),
    inference(splitLeft,[status(thm)],[c_191]) ).

tff(c_26,plain,
    subgroup_member(b),
    inference(cnfTransformation,[status(thm)],[f_149]) ).

tff(c_12,plain,
    ! [X_10] : ( multiply(X_10,identity) = X_10 ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_4,plain,
    ! [X_2] : ( multiply(inverse(X_2),X_2) = identity ),
    inference(cnfTransformation,[status(thm)],[f_76]) ).

tff(c_28,plain,
    multiply(b,inverse(a)) = c,
    inference(cnfTransformation,[status(thm)],[f_150]) ).

tff(c_197,plain,
    ! [X_28,Y_29,Z_30] : ( multiply(multiply(X_28,Y_29),Z_30) = multiply(X_28,multiply(Y_29,Z_30)) ),
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_590,plain,
    ! [Z_40] : ( multiply(b,multiply(inverse(a),Z_40)) = multiply(c,Z_40) ),
    inference(superposition,[status(thm),theory(equality)],[c_28,c_197]) ).

tff(c_624,plain,
    multiply(c,a) = multiply(b,identity),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_590]) ).

tff(c_640,plain,
    multiply(c,a) = b,
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_624]) ).

tff(c_2,plain,
    ! [X_1] : ( multiply(identity,X_1) = X_1 ),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_226,plain,
    ! [X_2,Z_30] : ( multiply(inverse(X_2),multiply(X_2,Z_30)) = multiply(identity,Z_30) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_197]) ).

tff(c_252,plain,
    ! [X_2,Z_30] : ( multiply(inverse(X_2),multiply(X_2,Z_30)) = Z_30 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_226]) ).

tff(c_649,plain,
    multiply(inverse(c),b) = a,
    inference(superposition,[status(thm),theory(equality)],[c_640,c_252]) ).

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_121]) ).

tff(c_673,plain,
    ( subgroup_member(a)
    | ~ subgroup_member(b)
    | ~ subgroup_member(inverse(c)) ),
    inference(superposition,[status(thm),theory(equality)],[c_649,c_10]) ).

tff(c_679,plain,
    ( subgroup_member(a)
    | ~ subgroup_member(inverse(c)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_673]) ).

tff(c_680,plain,
    ~ subgroup_member(inverse(c)),
    inference(negUnitSimplification,[status(thm)],[c_195,c_679]) ).

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_79]) ).

tff(c_397,plain,
    ! [X_35,Y_36] :
      ( ( multiply(X_35,element_in_O2(X_35,Y_36)) = Y_36 )
      | subgroup_member(Y_36)
      | subgroup_member(X_35) ),
    inference(cnfTransformation,[status(thm)],[f_147]) ).

tff(c_3121,plain,
    ! [X_69,Y_70,Y_71] :
      ( ( multiply(X_69,multiply(Y_70,element_in_O2(multiply(X_69,Y_70),Y_71))) = Y_71 )
      | subgroup_member(Y_71)
      | subgroup_member(multiply(X_69,Y_70)) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_397]) ).

tff(c_243,plain,
    ! [Z_30] : ( multiply(a,multiply(c,Z_30)) = multiply(d,Z_30) ),
    inference(superposition,[status(thm),theory(equality)],[c_30,c_197]) ).

tff(c_3201,plain,
    ! [Y_71] :
      ( ( multiply(d,element_in_O2(multiply(a,c),Y_71)) = Y_71 )
      | subgroup_member(Y_71)
      | subgroup_member(multiply(a,c)) ),
    inference(superposition,[status(thm),theory(equality)],[c_3121,c_243]) ).

tff(c_3413,plain,
    ! [Y_71] :
      ( ( multiply(d,element_in_O2(d,Y_71)) = Y_71 )
      | subgroup_member(Y_71)
      | subgroup_member(d) ),
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_30,c_3201]) ).

tff(c_3491,plain,
    ! [Y_72] :
      ( ( multiply(d,element_in_O2(d,Y_72)) = Y_72 )
      | subgroup_member(Y_72) ),
    inference(negUnitSimplification,[status(thm)],[c_32,c_3413]) ).

tff(c_4816,plain,
    ! [Y_93] :
      ( ( multiply(inverse(d),Y_93) = element_in_O2(d,Y_93) )
      | subgroup_member(Y_93) ),
    inference(superposition,[status(thm),theory(equality)],[c_3491,c_252]) ).

tff(c_14,plain,
    ! [X_11] : ( multiply(X_11,inverse(X_11)) = identity ),
    inference(cnfTransformation,[status(thm)],[f_128]) ).

tff(c_520,plain,
    ! [Z_39] : ( multiply(a,multiply(c,Z_39)) = multiply(d,Z_39) ),
    inference(superposition,[status(thm),theory(equality)],[c_30,c_197]) ).

tff(c_547,plain,
    multiply(d,inverse(c)) = multiply(a,identity),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_520]) ).

tff(c_556,plain,
    multiply(d,inverse(c)) = a,
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_547]) ).

tff(c_561,plain,
    multiply(inverse(d),a) = inverse(c),
    inference(superposition,[status(thm),theory(equality)],[c_556,c_252]) ).

tff(c_4916,plain,
    ( ( element_in_O2(d,a) = inverse(c) )
    | subgroup_member(a) ),
    inference(superposition,[status(thm),theory(equality)],[c_4816,c_561]) ).

tff(c_5020,plain,
    element_in_O2(d,a) = inverse(c),
    inference(negUnitSimplification,[status(thm)],[c_195,c_4916]) ).

tff(c_22,plain,
    ! [X_13,Y_14] :
      ( subgroup_member(element_in_O2(X_13,Y_14))
      | subgroup_member(Y_14)
      | subgroup_member(X_13) ),
    inference(cnfTransformation,[status(thm)],[f_141]) ).

tff(c_5212,plain,
    ( subgroup_member(inverse(c))
    | subgroup_member(a)
    | subgroup_member(d) ),
    inference(superposition,[status(thm),theory(equality)],[c_5020,c_22]) ).

tff(c_5222,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_32,c_195,c_680,c_5212]) ).

tff(c_5224,plain,
    subgroup_member(a),
    inference(splitRight,[status(thm)],[c_191]) ).

tff(c_8,plain,
    ! [X_6] :
      ( subgroup_member(inverse(X_6))
      | ~ subgroup_member(X_6) ),
    inference(cnfTransformation,[status(thm)],[f_110]) ).

tff(c_5223,plain,
    ~ subgroup_member(c),
    inference(splitRight,[status(thm)],[c_191]) ).

tff(c_169,plain,
    ( subgroup_member(c)
    | ~ subgroup_member(inverse(a))
    | ~ subgroup_member(b) ),
    inference(superposition,[status(thm),theory(equality)],[c_28,c_166]) ).

tff(c_186,plain,
    ( subgroup_member(c)
    | ~ subgroup_member(inverse(a)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_169]) ).

tff(c_5225,plain,
    ~ subgroup_member(inverse(a)),
    inference(negUnitSimplification,[status(thm)],[c_5223,c_186]) ).

tff(c_5228,plain,
    ~ subgroup_member(a),
    inference(resolution,[status(thm)],[c_8,c_5225]) ).

tff(c_5232,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_5224,c_5228]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : GRP039-7 : TPTP v8.1.2. Bugfixed v1.0.1.
% 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
% 0.15/0.36  % Computer : n019.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 22:00:46 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 6.28/2.52  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.28/2.53  
% 6.28/2.53  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.28/2.56  
% 6.28/2.56  Inference rules
% 6.28/2.56  ----------------------
% 6.28/2.56  #Ref     : 0
% 6.28/2.56  #Sup     : 1265
% 6.28/2.56  #Fact    : 0
% 6.28/2.56  #Define  : 0
% 6.63/2.56  #Split   : 4
% 6.63/2.56  #Chain   : 0
% 6.63/2.56  #Close   : 0
% 6.63/2.56  
% 6.63/2.56  Ordering : KBO
% 6.63/2.56  
% 6.63/2.56  Simplification rules
% 6.63/2.56  ----------------------
% 6.63/2.56  #Subsume      : 250
% 6.63/2.56  #Demod        : 1119
% 6.63/2.56  #Tautology    : 603
% 6.63/2.56  #SimpNegUnit  : 159
% 6.63/2.56  #BackRed      : 4
% 6.63/2.56  
% 6.63/2.56  #Partial instantiations: 0
% 6.63/2.56  #Strategies tried      : 1
% 6.63/2.56  
% 6.63/2.56  Timing (in seconds)
% 6.63/2.56  ----------------------
% 6.63/2.57  Preprocessing        : 0.47
% 6.63/2.57  Parsing              : 0.23
% 6.63/2.57  CNF conversion       : 0.02
% 6.63/2.57  Main loop            : 1.01
% 6.63/2.57  Inferencing          : 0.36
% 6.63/2.57  Reduction            : 0.37
% 6.63/2.57  Demodulation         : 0.28
% 6.63/2.57  BG Simplification    : 0.05
% 6.63/2.57  Subsumption          : 0.16
% 6.63/2.57  Abstraction          : 0.04
% 6.63/2.57  MUC search           : 0.00
% 6.63/2.57  Cooper               : 0.00
% 6.63/2.57  Total                : 1.54
% 6.63/2.57  Index Insertion      : 0.00
% 6.63/2.57  Index Deletion       : 0.00
% 6.63/2.57  Index Matching       : 0.00
% 6.63/2.57  BG Taut test         : 0.00
%------------------------------------------------------------------------------