TSTP Solution File: GRP039-3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP039-3 : 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/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 : n007.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 6.79s 2.59s
% Output   : CNFRefutation 6.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   87 (  36 unt;  10 typ;   0 def)
%            Number of atoms       :  154 (  21 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  146 (  69   ~;  77   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   5   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :  106 (; 106   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ product > 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(product,type,
    product: ( $i * $i * $i ) > $o ).

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_186,axiom,
    subgroup_member(b),
    file(unknown,unknown) ).

tff(f_171,axiom,
    ! [A] :
      ( ~ subgroup_member(A)
      | subgroup_member(inverse(A)) ),
    file(unknown,unknown) ).

tff(f_190,axiom,
    ~ subgroup_member(d),
    file(unknown,unknown) ).

tff(f_184,axiom,
    ! [A,B] :
      ( product(A,element_in_O2(A,B),B)
      | subgroup_member(B)
      | subgroup_member(A) ),
    file(unknown,unknown) ).

tff(f_188,axiom,
    product(a,c,d),
    file(unknown,unknown) ).

tff(f_155,axiom,
    ! [A,B,C,D] :
      ( ~ product(A,B,C)
      | ~ product(A,D,C)
      | ( D = B ) ),
    file(unknown,unknown) ).

tff(f_187,axiom,
    product(b,inverse(a),c),
    file(unknown,unknown) ).

tff(f_144,axiom,
    ! [A,B,C] :
      ( ~ subgroup_member(A)
      | ~ subgroup_member(B)
      | ~ product(A,inverse(B),C)
      | subgroup_member(C) ),
    file(unknown,unknown) ).

tff(f_77,axiom,
    ! [X,Y] : product(X,Y,multiply(X,Y)),
    file(unknown,unknown) ).

tff(f_86,axiom,
    ! [X,Y,Z,W] :
      ( ~ product(X,Y,Z)
      | ~ product(X,Y,W)
      | ( Z = W ) ),
    file(unknown,unknown) ).

tff(f_165,axiom,
    ! [A] : ( inverse(inverse(A)) = A ),
    file(unknown,unknown) ).

tff(f_74,axiom,
    ! [X] : product(X,inverse(X),identity),
    file(unknown,unknown) ).

tff(f_70,axiom,
    ! [X] : product(X,identity,X),
    file(unknown,unknown) ).

tff(f_108,axiom,
    ! [W,U,Z,X,Y,V] :
      ( ~ product(X,Y,U)
      | ~ product(Y,Z,V)
      | ~ product(X,V,W)
      | product(U,Z,W) ),
    file(unknown,unknown) ).

tff(f_178,axiom,
    ! [A,B] :
      ( subgroup_member(element_in_O2(A,B))
      | subgroup_member(B)
      | subgroup_member(A) ),
    file(unknown,unknown) ).

tff(f_72,axiom,
    ! [X] : product(inverse(X),X,identity),
    file(unknown,unknown) ).

tff(f_163,axiom,
    ! [A,B,C,D] :
      ( ~ product(A,B,C)
      | ~ product(D,B,C)
      | ( D = A ) ),
    file(unknown,unknown) ).

tff(f_68,axiom,
    ! [X] : product(identity,X,X),
    file(unknown,unknown) ).

tff(f_97,axiom,
    ! [W,U,Z,X,Y,V] :
      ( ~ product(X,Y,U)
      | ~ product(Y,Z,V)
      | ~ product(U,Z,W)
      | product(X,V,W) ),
    file(unknown,unknown) ).

tff(c_34,plain,
    subgroup_member(b),
    inference(cnfTransformation,[status(thm)],[f_186]) ).

tff(c_28,plain,
    ! [A_35] :
      ( subgroup_member(inverse(A_35))
      | ~ subgroup_member(A_35) ),
    inference(cnfTransformation,[status(thm)],[f_171]) ).

tff(c_40,plain,
    ~ subgroup_member(d),
    inference(cnfTransformation,[status(thm)],[f_190]) ).

tff(c_32,plain,
    ! [A_38,B_39] :
      ( subgroup_member(A_38)
      | subgroup_member(B_39)
      | product(A_38,element_in_O2(A_38,B_39),B_39) ),
    inference(cnfTransformation,[status(thm)],[f_184]) ).

tff(c_38,plain,
    product(a,c,d),
    inference(cnfTransformation,[status(thm)],[f_188]) ).

tff(c_310,plain,
    ! [D_72,B_73,A_74,C_75] :
      ( ( D_72 = B_73 )
      | ~ product(A_74,D_72,C_75)
      | ~ product(A_74,B_73,C_75) ),
    inference(cnfTransformation,[status(thm)],[f_155]) ).

tff(c_335,plain,
    ! [B_76] :
      ( ( c = B_76 )
      | ~ product(a,B_76,d) ),
    inference(resolution,[status(thm)],[c_38,c_310]) ).

tff(c_339,plain,
    ( ( element_in_O2(a,d) = c )
    | subgroup_member(a)
    | subgroup_member(d) ),
    inference(resolution,[status(thm)],[c_32,c_335]) ).

tff(c_345,plain,
    ( ( element_in_O2(a,d) = c )
    | subgroup_member(a) ),
    inference(negUnitSimplification,[status(thm)],[c_40,c_339]) ).

tff(c_371,plain,
    subgroup_member(a),
    inference(splitLeft,[status(thm)],[c_345]) ).

tff(c_36,plain,
    product(b,inverse(a),c),
    inference(cnfTransformation,[status(thm)],[f_187]) ).

tff(c_394,plain,
    ! [C_80,A_81,B_82] :
      ( subgroup_member(C_80)
      | ~ product(A_81,inverse(B_82),C_80)
      | ~ subgroup_member(B_82)
      | ~ subgroup_member(A_81) ),
    inference(cnfTransformation,[status(thm)],[f_144]) ).

tff(c_411,plain,
    ( subgroup_member(c)
    | ~ subgroup_member(a)
    | ~ subgroup_member(b) ),
    inference(resolution,[status(thm)],[c_36,c_394]) ).

tff(c_428,plain,
    subgroup_member(c),
    inference(demodulation,[status(thm),theory(equality)],[c_34,c_371,c_411]) ).

tff(c_10,plain,
    ! [X_5,Y_6] : product(X_5,Y_6,multiply(X_5,Y_6)),
    inference(cnfTransformation,[status(thm)],[f_77]) ).

tff(c_84,plain,
    ! [Z_51,W_52,X_53,Y_54] :
      ( ( Z_51 = W_52 )
      | ~ product(X_53,Y_54,W_52)
      | ~ product(X_53,Y_54,Z_51) ),
    inference(cnfTransformation,[status(thm)],[f_86]) ).

tff(c_177,plain,
    ! [Z_60] :
      ( ( d = Z_60 )
      | ~ product(a,c,Z_60) ),
    inference(resolution,[status(thm)],[c_38,c_84]) ).

tff(c_185,plain,
    multiply(a,c) = d,
    inference(resolution,[status(thm)],[c_10,c_177]) ).

tff(c_24,plain,
    ! [A_34] : ( inverse(inverse(A_34)) = A_34 ),
    inference(cnfTransformation,[status(thm)],[f_165]) ).

tff(c_825,plain,
    ! [X_120,B_121] :
      ( subgroup_member(multiply(X_120,inverse(B_121)))
      | ~ subgroup_member(B_121)
      | ~ subgroup_member(X_120) ),
    inference(resolution,[status(thm)],[c_10,c_394]) ).

tff(c_879,plain,
    ! [X_124,A_125] :
      ( subgroup_member(multiply(X_124,A_125))
      | ~ subgroup_member(inverse(A_125))
      | ~ subgroup_member(X_124) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_825]) ).

tff(c_894,plain,
    ( subgroup_member(d)
    | ~ subgroup_member(inverse(c))
    | ~ subgroup_member(a) ),
    inference(superposition,[status(thm),theory(equality)],[c_185,c_879]) ).

tff(c_905,plain,
    ( subgroup_member(d)
    | ~ subgroup_member(inverse(c)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_371,c_894]) ).

tff(c_906,plain,
    ~ subgroup_member(inverse(c)),
    inference(negUnitSimplification,[status(thm)],[c_40,c_905]) ).

tff(c_912,plain,
    ~ subgroup_member(c),
    inference(resolution,[status(thm)],[c_28,c_906]) ).

tff(c_916,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_428,c_912]) ).

tff(c_918,plain,
    ~ subgroup_member(a),
    inference(splitRight,[status(thm)],[c_345]) ).

tff(c_8,plain,
    ! [X_4] : product(X_4,inverse(X_4),identity),
    inference(cnfTransformation,[status(thm)],[f_74]) ).

tff(c_4,plain,
    ! [X_2] : product(X_2,identity,X_2),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_1082,plain,
    ! [V_141,X_139,U_140,Y_138,Z_143,W_142] :
      ( product(U_140,Z_143,W_142)
      | ~ product(X_139,V_141,W_142)
      | ~ product(Y_138,Z_143,V_141)
      | ~ product(X_139,Y_138,U_140) ),
    inference(cnfTransformation,[status(thm)],[f_108]) ).

tff(c_1621,plain,
    ! [U_185,Z_186,X_187,Y_188] :
      ( product(U_185,Z_186,X_187)
      | ~ product(Y_188,Z_186,identity)
      | ~ product(X_187,Y_188,U_185) ),
    inference(resolution,[status(thm)],[c_4,c_1082]) ).

tff(c_1661,plain,
    ! [U_191,X_192,X_193] :
      ( product(U_191,inverse(X_192),X_193)
      | ~ product(X_193,X_192,U_191) ),
    inference(resolution,[status(thm)],[c_8,c_1621]) ).

tff(c_333,plain,
    ! [B_73] :
      ( ( c = B_73 )
      | ~ product(a,B_73,d) ),
    inference(resolution,[status(thm)],[c_38,c_310]) ).

tff(c_1884,plain,
    ! [X_201] :
      ( ( inverse(X_201) = c )
      | ~ product(d,X_201,a) ),
    inference(resolution,[status(thm)],[c_1661,c_333]) ).

tff(c_1892,plain,
    ( ( inverse(element_in_O2(d,a)) = c )
    | subgroup_member(d)
    | subgroup_member(a) ),
    inference(resolution,[status(thm)],[c_32,c_1884]) ).

tff(c_1897,plain,
    inverse(element_in_O2(d,a)) = c,
    inference(negUnitSimplification,[status(thm)],[c_918,c_40,c_1892]) ).

tff(c_1967,plain,
    element_in_O2(d,a) = inverse(c),
    inference(superposition,[status(thm),theory(equality)],[c_1897,c_24]) ).

tff(c_30,plain,
    ! [A_36,B_37] :
      ( subgroup_member(A_36)
      | subgroup_member(B_37)
      | subgroup_member(element_in_O2(A_36,B_37)) ),
    inference(cnfTransformation,[status(thm)],[f_178]) ).

tff(c_1992,plain,
    ( subgroup_member(d)
    | subgroup_member(a)
    | subgroup_member(inverse(c)) ),
    inference(superposition,[status(thm),theory(equality)],[c_1967,c_30]) ).

tff(c_1999,plain,
    subgroup_member(inverse(c)),
    inference(negUnitSimplification,[status(thm)],[c_918,c_40,c_1992]) ).

tff(c_6,plain,
    ! [X_3] : product(inverse(X_3),X_3,identity),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_253,plain,
    ! [D_65,A_66,B_67,C_68] :
      ( ( D_65 = A_66 )
      | ~ product(D_65,B_67,C_68)
      | ~ product(A_66,B_67,C_68) ),
    inference(cnfTransformation,[status(thm)],[f_163]) ).

tff(c_274,plain,
    ! [A_66] :
      ( ( b = A_66 )
      | ~ product(A_66,inverse(a),c) ),
    inference(resolution,[status(thm)],[c_36,c_253]) ).

tff(c_1804,plain,
    ! [U_198] :
      ( ( b = U_198 )
      | ~ product(c,a,U_198) ),
    inference(resolution,[status(thm)],[c_1661,c_274]) ).

tff(c_1809,plain,
    multiply(c,a) = b,
    inference(resolution,[status(thm)],[c_10,c_1804]) ).

tff(c_1822,plain,
    product(c,a,b),
    inference(superposition,[status(thm),theory(equality)],[c_1809,c_10]) ).

tff(c_2,plain,
    ! [X_1] : product(identity,X_1,X_1),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_996,plain,
    ! [Z_134,Y_131,X_133,V_135,U_132,W_130] :
      ( product(X_133,V_135,W_130)
      | ~ product(U_132,Z_134,W_130)
      | ~ product(Y_131,Z_134,V_135)
      | ~ product(X_133,Y_131,U_132) ),
    inference(cnfTransformation,[status(thm)],[f_97]) ).

tff(c_2509,plain,
    ! [X_231,V_232,X_233,Y_234] :
      ( product(X_231,V_232,X_233)
      | ~ product(Y_234,X_233,V_232)
      | ~ product(X_231,Y_234,identity) ),
    inference(resolution,[status(thm)],[c_2,c_996]) ).

tff(c_4657,plain,
    ! [X_323] :
      ( product(X_323,b,a)
      | ~ product(X_323,c,identity) ),
    inference(resolution,[status(thm)],[c_1822,c_2509]) ).

tff(c_4666,plain,
    product(inverse(c),b,a),
    inference(resolution,[status(thm)],[c_6,c_4657]) ).

tff(c_919,plain,
    ! [C_126,A_127,B_128] :
      ( subgroup_member(C_126)
      | ~ product(A_127,inverse(B_128),C_126)
      | ~ subgroup_member(B_128)
      | ~ subgroup_member(A_127) ),
    inference(cnfTransformation,[status(thm)],[f_144]) ).

tff(c_943,plain,
    ! [C_126,A_127,A_34] :
      ( subgroup_member(C_126)
      | ~ product(A_127,A_34,C_126)
      | ~ subgroup_member(inverse(A_34))
      | ~ subgroup_member(A_127) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_919]) ).

tff(c_4695,plain,
    ( subgroup_member(a)
    | ~ subgroup_member(inverse(b))
    | ~ subgroup_member(inverse(c)) ),
    inference(resolution,[status(thm)],[c_4666,c_943]) ).

tff(c_4728,plain,
    ( subgroup_member(a)
    | ~ subgroup_member(inverse(b)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1999,c_4695]) ).

tff(c_4729,plain,
    ~ subgroup_member(inverse(b)),
    inference(negUnitSimplification,[status(thm)],[c_918,c_4728]) ).

tff(c_4739,plain,
    ~ subgroup_member(b),
    inference(resolution,[status(thm)],[c_28,c_4729]) ).

tff(c_4743,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_34,c_4739]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : GRP039-3 : TPTP v8.1.2. Released v1.0.0.
% 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 : n007.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 21:55:54 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 6.79/2.59  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.79/2.61  
% 6.79/2.61  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.93/2.65  
% 6.93/2.65  Inference rules
% 6.93/2.65  ----------------------
% 6.93/2.65  #Ref     : 0
% 6.93/2.65  #Sup     : 1097
% 6.93/2.65  #Fact    : 0
% 6.93/2.65  #Define  : 0
% 6.93/2.65  #Split   : 21
% 6.93/2.65  #Chain   : 0
% 6.93/2.65  #Close   : 0
% 6.93/2.65  
% 6.93/2.65  Ordering : KBO
% 6.93/2.65  
% 6.93/2.65  Simplification rules
% 6.93/2.65  ----------------------
% 6.93/2.65  #Subsume      : 222
% 6.93/2.65  #Demod        : 457
% 6.93/2.65  #Tautology    : 391
% 6.93/2.65  #SimpNegUnit  : 60
% 6.93/2.65  #BackRed      : 2
% 6.93/2.65  
% 6.93/2.65  #Partial instantiations: 0
% 6.93/2.65  #Strategies tried      : 1
% 6.93/2.65  
% 6.93/2.65  Timing (in seconds)
% 6.93/2.65  ----------------------
% 6.93/2.65  Preprocessing        : 0.50
% 6.93/2.65  Parsing              : 0.27
% 6.93/2.65  CNF conversion       : 0.03
% 6.93/2.65  Main loop            : 1.07
% 6.93/2.65  Inferencing          : 0.39
% 6.93/2.65  Reduction            : 0.30
% 6.93/2.65  Demodulation         : 0.21
% 6.93/2.65  BG Simplification    : 0.03
% 6.93/2.65  Subsumption          : 0.26
% 6.93/2.65  Abstraction          : 0.04
% 6.93/2.65  MUC search           : 0.00
% 6.93/2.65  Cooper               : 0.00
% 6.93/2.65  Total                : 1.63
% 6.93/2.65  Index Insertion      : 0.00
% 6.93/2.65  Index Deletion       : 0.00
% 6.93/2.65  Index Matching       : 0.00
% 6.93/2.65  BG Taut test         : 0.00
%------------------------------------------------------------------------------