TSTP Solution File: GRP040-4 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP040-4 : 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 : n006.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 10:39:43 EDT 2023

% Result   : Unsatisfiable 6.54s 2.63s
% Output   : CNFRefutation 6.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   76 (  33 unt;  10 typ;   0 def)
%            Number of atoms       :  130 (  20 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  120 (  56   ~;  64   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   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   :  108 (; 108   !;   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_168,axiom,
    subgroup_member(b),
    file(unknown,unknown) ).

tff(f_136,axiom,
    ! [A] :
      ( ~ subgroup_member(A)
      | subgroup_member(inverse(A)) ),
    file(unknown,unknown) ).

tff(f_167,axiom,
    ~ subgroup_member(a),
    file(unknown,unknown) ).

tff(f_170,axiom,
    ~ subgroup_member(d),
    file(unknown,unknown) ).

tff(f_60,axiom,
    ! [X,Y] : product(X,Y,multiply(X,Y)),
    file(unknown,unknown) ).

tff(f_55,axiom,
    ! [X] : product(inverse(X),X,identity),
    file(unknown,unknown) ).

tff(f_53,axiom,
    ! [X] : product(X,identity,X),
    file(unknown,unknown) ).

tff(f_91,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_172,axiom,
    product(a,c,d),
    file(unknown,unknown) ).

tff(f_152,axiom,
    ! [A,B,C,D] :
      ( ~ product(A,B,C)
      | ~ product(D,B,C)
      | ( D = A ) ),
    file(unknown,unknown) ).

tff(f_165,axiom,
    ! [A,B] :
      ( product(A,element_in_O2(A,B),B)
      | subgroup_member(B)
      | subgroup_member(A) ),
    file(unknown,unknown) ).

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

tff(f_159,axiom,
    ! [A,B] :
      ( subgroup_member(element_in_O2(A,B))
      | subgroup_member(B)
      | subgroup_member(A) ),
    file(unknown,unknown) ).

tff(f_171,axiom,
    product(b,inverse(a),c),
    file(unknown,unknown) ).

tff(f_57,axiom,
    ! [X] : product(X,inverse(X),identity),
    file(unknown,unknown) ).

tff(f_80,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(f_174,axiom,
    ! [A] : ( inverse(inverse(A)) = A ),
    file(unknown,unknown) ).

tff(f_69,axiom,
    ! [X,Y,Z,W] :
      ( ~ product(X,Y,Z)
      | ~ product(X,Y,W)
      | ( Z = W ) ),
    file(unknown,unknown) ).

tff(f_127,axiom,
    ! [A,B,C] :
      ( ~ subgroup_member(A)
      | ~ subgroup_member(B)
      | ~ product(A,inverse(B),C)
      | subgroup_member(C) ),
    file(unknown,unknown) ).

tff(c_34,plain,
    subgroup_member(b),
    inference(cnfTransformation,[status(thm)],[f_168]) ).

tff(c_22,plain,
    ! [A_26] :
      ( subgroup_member(inverse(A_26))
      | ~ subgroup_member(A_26) ),
    inference(cnfTransformation,[status(thm)],[f_136]) ).

tff(c_32,plain,
    ~ subgroup_member(a),
    inference(cnfTransformation,[status(thm)],[f_167]) ).

tff(c_36,plain,
    ~ subgroup_member(d),
    inference(cnfTransformation,[status(thm)],[f_170]) ).

tff(c_10,plain,
    ! [X_5,Y_6] : product(X_5,Y_6,multiply(X_5,Y_6)),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_6,plain,
    ! [X_3] : product(inverse(X_3),X_3,identity),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_4,plain,
    ! [X_2] : product(X_2,identity,X_2),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_494,plain,
    ! [V_89,X_87,U_88,W_90,Z_91,Y_86] :
      ( product(U_88,Z_91,W_90)
      | ~ product(X_87,V_89,W_90)
      | ~ product(Y_86,Z_91,V_89)
      | ~ product(X_87,Y_86,U_88) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

tff(c_1878,plain,
    ! [U_171,Z_172,X_173,Y_174] :
      ( product(U_171,Z_172,X_173)
      | ~ product(Y_174,Z_172,identity)
      | ~ product(X_173,Y_174,U_171) ),
    inference(resolution,[status(thm)],[c_4,c_494]) ).

tff(c_2088,plain,
    ! [U_180,X_181,X_182] :
      ( product(U_180,X_181,X_182)
      | ~ product(X_182,inverse(X_181),U_180) ),
    inference(resolution,[status(thm)],[c_6,c_1878]) ).

tff(c_2231,plain,
    ! [X_189,X_190] : product(multiply(X_189,inverse(X_190)),X_190,X_189),
    inference(resolution,[status(thm)],[c_10,c_2088]) ).

tff(c_40,plain,
    product(a,c,d),
    inference(cnfTransformation,[status(thm)],[f_172]) ).

tff(c_86,plain,
    ! [D_51,A_52,B_53,C_54] :
      ( ( D_51 = A_52 )
      | ~ product(D_51,B_53,C_54)
      | ~ product(A_52,B_53,C_54) ),
    inference(cnfTransformation,[status(thm)],[f_152]) ).

tff(c_106,plain,
    ! [A_52] :
      ( ( a = A_52 )
      | ~ product(A_52,c,d) ),
    inference(resolution,[status(thm)],[c_40,c_86]) ).

tff(c_2377,plain,
    multiply(d,inverse(c)) = a,
    inference(resolution,[status(thm)],[c_2231,c_106]) ).

tff(c_2407,plain,
    product(d,inverse(c),a),
    inference(superposition,[status(thm),theory(equality)],[c_2377,c_10]) ).

tff(c_30,plain,
    ! [A_37,B_38] :
      ( subgroup_member(A_37)
      | subgroup_member(B_38)
      | product(A_37,element_in_O2(A_37,B_38),B_38) ),
    inference(cnfTransformation,[status(thm)],[f_165]) ).

tff(c_244,plain,
    ! [D_67,B_68,A_69,C_70] :
      ( ( D_67 = B_68 )
      | ~ product(A_69,D_67,C_70)
      | ~ product(A_69,B_68,C_70) ),
    inference(cnfTransformation,[status(thm)],[f_144]) ).

tff(c_261,plain,
    ! [A_37,B_38,B_68] :
      ( ( element_in_O2(A_37,B_38) = B_68 )
      | ~ product(A_37,B_68,B_38)
      | subgroup_member(A_37)
      | subgroup_member(B_38) ),
    inference(resolution,[status(thm)],[c_30,c_244]) ).

tff(c_2428,plain,
    ( ( element_in_O2(d,a) = inverse(c) )
    | subgroup_member(d)
    | subgroup_member(a) ),
    inference(resolution,[status(thm)],[c_2407,c_261]) ).

tff(c_2452,plain,
    element_in_O2(d,a) = inverse(c),
    inference(negUnitSimplification,[status(thm)],[c_32,c_36,c_2428]) ).

tff(c_28,plain,
    ! [A_35,B_36] :
      ( subgroup_member(A_35)
      | subgroup_member(B_36)
      | subgroup_member(element_in_O2(A_35,B_36)) ),
    inference(cnfTransformation,[status(thm)],[f_159]) ).

tff(c_2483,plain,
    ( subgroup_member(d)
    | subgroup_member(a)
    | subgroup_member(inverse(c)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2452,c_28]) ).

tff(c_2492,plain,
    subgroup_member(inverse(c)),
    inference(negUnitSimplification,[status(thm)],[c_32,c_36,c_2483]) ).

tff(c_2121,plain,
    ! [X_5,X_181] : product(multiply(X_5,inverse(X_181)),X_181,X_5),
    inference(resolution,[status(thm)],[c_10,c_2088]) ).

tff(c_38,plain,
    product(b,inverse(a),c),
    inference(cnfTransformation,[status(thm)],[f_171]) ).

tff(c_8,plain,
    ! [X_4] : product(X_4,inverse(X_4),identity),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_607,plain,
    ! [Z_101,Y_98,X_100,W_97,U_99,V_102] :
      ( product(X_100,V_102,W_97)
      | ~ product(U_99,Z_101,W_97)
      | ~ product(Y_98,Z_101,V_102)
      | ~ product(X_100,Y_98,U_99) ),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_3613,plain,
    ! [X_227,V_228,Y_229,X_230] :
      ( product(X_227,V_228,identity)
      | ~ product(Y_229,inverse(X_230),V_228)
      | ~ product(X_227,Y_229,X_230) ),
    inference(resolution,[status(thm)],[c_8,c_607]) ).

tff(c_3865,plain,
    ! [X_238] :
      ( product(X_238,c,identity)
      | ~ product(X_238,b,a) ),
    inference(resolution,[status(thm)],[c_38,c_3613]) ).

tff(c_263,plain,
    ! [X_4,B_68] :
      ( ( inverse(X_4) = B_68 )
      | ~ product(X_4,B_68,identity) ),
    inference(resolution,[status(thm)],[c_8,c_244]) ).

tff(c_3972,plain,
    ! [X_239] :
      ( ( inverse(X_239) = c )
      | ~ product(X_239,b,a) ),
    inference(resolution,[status(thm)],[c_3865,c_263]) ).

tff(c_3977,plain,
    inverse(multiply(a,inverse(b))) = c,
    inference(resolution,[status(thm)],[c_2121,c_3972]) ).

tff(c_42,plain,
    ! [A_39] : ( inverse(inverse(A_39)) = A_39 ),
    inference(cnfTransformation,[status(thm)],[f_174]) ).

tff(c_4132,plain,
    multiply(a,inverse(b)) = inverse(c),
    inference(superposition,[status(thm),theory(equality)],[c_3977,c_42]) ).

tff(c_318,plain,
    ! [Z_74,W_75,X_76,Y_77] :
      ( ( Z_74 = W_75 )
      | ~ product(X_76,Y_77,W_75)
      | ~ product(X_76,Y_77,Z_74) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_336,plain,
    ! [X_5,Y_6,Z_74] :
      ( ( multiply(X_5,Y_6) = Z_74 )
      | ~ product(X_5,Y_6,Z_74) ),
    inference(resolution,[status(thm)],[c_10,c_318]) ).

tff(c_2359,plain,
    ! [X_189,X_190] : ( multiply(multiply(X_189,inverse(X_190)),X_190) = X_189 ),
    inference(resolution,[status(thm)],[c_2231,c_336]) ).

tff(c_4155,plain,
    multiply(inverse(c),b) = a,
    inference(superposition,[status(thm),theory(equality)],[c_4132,c_2359]) ).

tff(c_414,plain,
    ! [C_82,A_83,B_84] :
      ( subgroup_member(C_82)
      | ~ product(A_83,inverse(B_84),C_82)
      | ~ subgroup_member(B_84)
      | ~ subgroup_member(A_83) ),
    inference(cnfTransformation,[status(thm)],[f_127]) ).

tff(c_884,plain,
    ! [X_122,B_123] :
      ( subgroup_member(multiply(X_122,inverse(B_123)))
      | ~ subgroup_member(B_123)
      | ~ subgroup_member(X_122) ),
    inference(resolution,[status(thm)],[c_10,c_414]) ).

tff(c_904,plain,
    ! [X_122,A_39] :
      ( subgroup_member(multiply(X_122,A_39))
      | ~ subgroup_member(inverse(A_39))
      | ~ subgroup_member(X_122) ),
    inference(superposition,[status(thm),theory(equality)],[c_42,c_884]) ).

tff(c_4262,plain,
    ( subgroup_member(a)
    | ~ subgroup_member(inverse(b))
    | ~ subgroup_member(inverse(c)) ),
    inference(superposition,[status(thm),theory(equality)],[c_4155,c_904]) ).

tff(c_4277,plain,
    ( subgroup_member(a)
    | ~ subgroup_member(inverse(b)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2492,c_4262]) ).

tff(c_4278,plain,
    ~ subgroup_member(inverse(b)),
    inference(negUnitSimplification,[status(thm)],[c_32,c_4277]) ).

tff(c_4286,plain,
    ~ subgroup_member(b),
    inference(resolution,[status(thm)],[c_22,c_4278]) ).

tff(c_4291,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_34,c_4286]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRP040-4 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % 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
% 0.13/0.34  % Computer : n006.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 22:07:44 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 6.54/2.63  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.54/2.64  
% 6.54/2.64  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.54/2.67  
% 6.54/2.67  Inference rules
% 6.54/2.67  ----------------------
% 6.54/2.67  #Ref     : 0
% 6.54/2.67  #Sup     : 997
% 6.54/2.67  #Fact    : 0
% 6.54/2.67  #Define  : 0
% 6.54/2.67  #Split   : 15
% 6.54/2.67  #Chain   : 0
% 6.54/2.67  #Close   : 0
% 6.54/2.67  
% 6.54/2.67  Ordering : KBO
% 6.54/2.67  
% 6.54/2.67  Simplification rules
% 6.54/2.67  ----------------------
% 6.54/2.67  #Subsume      : 193
% 6.54/2.67  #Demod        : 498
% 6.54/2.67  #Tautology    : 379
% 6.54/2.67  #SimpNegUnit  : 39
% 6.54/2.67  #BackRed      : 2
% 6.54/2.67  
% 6.54/2.67  #Partial instantiations: 0
% 6.54/2.68  #Strategies tried      : 1
% 6.54/2.68  
% 6.54/2.68  Timing (in seconds)
% 6.54/2.68  ----------------------
% 6.54/2.68  Preprocessing        : 0.51
% 6.54/2.68  Parsing              : 0.26
% 6.54/2.68  CNF conversion       : 0.03
% 6.54/2.68  Main loop            : 1.06
% 6.54/2.68  Inferencing          : 0.40
% 6.54/2.68  Reduction            : 0.31
% 6.54/2.68  Demodulation         : 0.21
% 6.54/2.68  BG Simplification    : 0.03
% 6.54/2.68  Subsumption          : 0.25
% 6.54/2.68  Abstraction          : 0.04
% 6.54/2.68  MUC search           : 0.00
% 6.54/2.68  Cooper               : 0.00
% 6.54/2.68  Total                : 1.63
% 6.54/2.68  Index Insertion      : 0.00
% 6.54/2.68  Index Deletion       : 0.00
% 6.54/2.68  Index Matching       : 0.00
% 6.54/2.68  BG Taut test         : 0.00
%------------------------------------------------------------------------------