TSTP Solution File: GRP128-4.003 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP128-4.003 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 : 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 10:40:11 EDT 2023

% Result   : Unsatisfiable 7.14s 2.65s
% Output   : CNFRefutation 7.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   20
% Syntax   : Number of formulae    :  102 (  49 unt;   6 typ;   0 def)
%            Number of atoms       :  195 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  177 (  78   ~;  99   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   72 (;  72   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ product > equalish > group_element > #nlpp > e_3 > e_2 > e_1

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(group_element,type,
    group_element: $i > $o ).

tff(e_2,type,
    e_2: $i ).

tff(product,type,
    product: ( $i * $i * $i ) > $o ).

tff(e_3,type,
    e_3: $i ).

tff(equalish,type,
    equalish: ( $i * $i ) > $o ).

tff(e_1,type,
    e_1: $i ).

tff(f_80,axiom,
    ~ equalish(e_2,e_3),
    file(unknown,unknown) ).

tff(f_71,axiom,
    group_element(e_2),
    file(unknown,unknown) ).

tff(f_72,axiom,
    group_element(e_3),
    file(unknown,unknown) ).

tff(f_41,axiom,
    ! [X,Y] :
      ( ~ group_element(X)
      | ~ group_element(Y)
      | product(e_1,X,Y)
      | product(e_2,X,Y)
      | product(e_3,X,Y) ),
    file(unknown,unknown) ).

tff(f_84,axiom,
    ~ equalish(e_3,e_2),
    file(unknown,unknown) ).

tff(f_96,axiom,
    ! [X,Y] :
      ( ~ group_element(X)
      | ~ group_element(Y)
      | product(X,Y,e_1)
      | product(X,Y,e_2)
      | product(X,Y,e_3) ),
    file(unknown,unknown) ).

tff(f_128,axiom,
    ! [X,Y,Z1,Z2] :
      ( ~ product(X,Y,Z1)
      | ~ product(Z1,Y,Z2)
      | product(X,Z1,Z2) ),
    file(unknown,unknown) ).

tff(f_112,axiom,
    ! [X,W,Y,Z] :
      ( ~ product(X,W,Y)
      | ~ product(X,Z,Y)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(f_76,axiom,
    ~ equalish(e_1,e_3),
    file(unknown,unknown) ).

tff(f_70,axiom,
    group_element(e_1),
    file(unknown,unknown) ).

tff(f_61,axiom,
    ! [X,Y,Z1,Z2] :
      ( product(X,Y,Z1)
      | ~ product(X,Z1,Z2)
      | ~ product(Z1,Y,Z2) ),
    file(unknown,unknown) ).

tff(f_104,axiom,
    ! [X,Y,W,Z] :
      ( ~ product(X,Y,W)
      | ~ product(X,Y,Z)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(f_69,axiom,
    ! [Z1,Y,Z2,X] :
      ( product(Z1,Y,Z2)
      | ~ product(X,Z1,Z2)
      | ~ product(X,Y,Z1) ),
    file(unknown,unknown) ).

tff(f_78,axiom,
    ~ equalish(e_2,e_1),
    file(unknown,unknown) ).

tff(c_22,plain,
    ~ equalish(e_2,e_3),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_12,plain,
    group_element(e_2),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_14,plain,
    group_element(e_3),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_2,plain,
    ! [X_1,Y_2] :
      ( product(e_3,X_1,Y_2)
      | product(e_2,X_1,Y_2)
      | product(e_1,X_1,Y_2)
      | ~ group_element(Y_2)
      | ~ group_element(X_1) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_26,plain,
    ~ equalish(e_3,e_2),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_81,plain,
    ! [X_59,Y_60] :
      ( product(X_59,Y_60,e_3)
      | product(X_59,Y_60,e_2)
      | product(X_59,Y_60,e_1)
      | ~ group_element(Y_60)
      | ~ group_element(X_59) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_36,plain,
    ! [X_27,Z1_29,Z2_30,Y_28] :
      ( product(X_27,Z1_29,Z2_30)
      | ~ product(Z1_29,Y_28,Z2_30)
      | ~ product(X_27,Y_28,Z1_29) ),
    inference(cnfTransformation,[status(thm)],[f_128]) ).

tff(c_349,plain,
    ! [X_109,X_110,Y_111] :
      ( product(X_109,X_110,e_3)
      | ~ product(X_109,Y_111,X_110)
      | product(X_110,Y_111,e_2)
      | product(X_110,Y_111,e_1)
      | ~ group_element(Y_111)
      | ~ group_element(X_110) ),
    inference(resolution,[status(thm)],[c_81,c_36]) ).

tff(c_362,plain,
    ! [Y_2,X_1] :
      ( product(e_3,Y_2,e_3)
      | product(Y_2,X_1,e_2)
      | product(Y_2,X_1,e_1)
      | product(e_2,X_1,Y_2)
      | product(e_1,X_1,Y_2)
      | ~ group_element(Y_2)
      | ~ group_element(X_1) ),
    inference(resolution,[status(thm)],[c_2,c_349]) ).

tff(c_549,plain,
    ! [X_1] :
      ( product(e_3,e_2,e_3)
      | product(e_2,X_1,e_1)
      | product(e_1,X_1,e_2)
      | ~ group_element(e_2)
      | ~ group_element(X_1)
      | product(e_2,X_1,e_2) ),
    inference(factorization,[status(thm),theory(equality)],[c_362]) ).

tff(c_552,plain,
    ! [X_1] :
      ( product(e_3,e_2,e_3)
      | product(e_2,X_1,e_1)
      | product(e_1,X_1,e_2)
      | ~ group_element(X_1)
      | product(e_2,X_1,e_2) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_549]) ).

tff(c_805,plain,
    product(e_3,e_2,e_3),
    inference(splitLeft,[status(thm)],[c_552]) ).

tff(c_1233,plain,
    ! [X_125] :
      ( product(X_125,e_3,e_3)
      | ~ product(X_125,e_2,e_3) ),
    inference(resolution,[status(thm)],[c_805,c_36]) ).

tff(c_32,plain,
    ! [W_20,Z_22,X_19,Y_21] :
      ( equalish(W_20,Z_22)
      | ~ product(X_19,Z_22,Y_21)
      | ~ product(X_19,W_20,Y_21) ),
    inference(cnfTransformation,[status(thm)],[f_112]) ).

tff(c_889,plain,
    ! [W_20] :
      ( equalish(W_20,e_2)
      | ~ product(e_3,W_20,e_3) ),
    inference(resolution,[status(thm)],[c_805,c_32]) ).

tff(c_1241,plain,
    ( equalish(e_3,e_2)
    | ~ product(e_3,e_2,e_3) ),
    inference(resolution,[status(thm)],[c_1233,c_889]) ).

tff(c_1298,plain,
    equalish(e_3,e_2),
    inference(demodulation,[status(thm),theory(equality)],[c_805,c_1241]) ).

tff(c_1300,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_26,c_1298]) ).

tff(c_1302,plain,
    ~ product(e_3,e_2,e_3),
    inference(splitRight,[status(thm)],[c_552]) ).

tff(c_1579,plain,
    ( product(e_2,e_2,e_3)
    | product(e_1,e_2,e_3)
    | ~ group_element(e_3)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_2,c_1302]) ).

tff(c_1591,plain,
    ( product(e_2,e_2,e_3)
    | product(e_1,e_2,e_3) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_14,c_1579]) ).

tff(c_2062,plain,
    product(e_1,e_2,e_3),
    inference(splitLeft,[status(thm)],[c_1591]) ).

tff(c_28,plain,
    ! [X_13,Y_14] :
      ( product(X_13,Y_14,e_3)
      | product(X_13,Y_14,e_2)
      | product(X_13,Y_14,e_1)
      | ~ group_element(Y_14)
      | ~ group_element(X_13) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_1576,plain,
    ( product(e_3,e_2,e_2)
    | product(e_3,e_2,e_1)
    | ~ group_element(e_2)
    | ~ group_element(e_3) ),
    inference(resolution,[status(thm)],[c_28,c_1302]) ).

tff(c_1588,plain,
    ( product(e_3,e_2,e_2)
    | product(e_3,e_2,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_12,c_1576]) ).

tff(c_1592,plain,
    product(e_3,e_2,e_1),
    inference(splitLeft,[status(thm)],[c_1588]) ).

tff(c_1654,plain,
    ! [X_27] :
      ( product(X_27,e_3,e_1)
      | ~ product(X_27,e_2,e_3) ),
    inference(resolution,[status(thm)],[c_1592,c_36]) ).

tff(c_18,plain,
    ~ equalish(e_1,e_3),
    inference(cnfTransformation,[status(thm)],[f_76]) ).

tff(c_10,plain,
    group_element(e_1),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_6,plain,
    ! [Z1_7,Y_6,Z2_8,X_5] :
      ( ~ product(Z1_7,Y_6,Z2_8)
      | ~ product(X_5,Z1_7,Z2_8)
      | product(X_5,Y_6,Z1_7) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_2440,plain,
    ! [X_139] :
      ( ~ product(X_139,e_1,e_3)
      | product(X_139,e_2,e_1) ),
    inference(resolution,[status(thm)],[c_2062,c_6]) ).

tff(c_30,plain,
    ! [W_17,Z_18,X_15,Y_16] :
      ( equalish(W_17,Z_18)
      | ~ product(X_15,Y_16,Z_18)
      | ~ product(X_15,Y_16,W_17) ),
    inference(cnfTransformation,[status(thm)],[f_104]) ).

tff(c_2131,plain,
    ! [W_17] :
      ( equalish(W_17,e_3)
      | ~ product(e_1,e_2,W_17) ),
    inference(resolution,[status(thm)],[c_2062,c_30]) ).

tff(c_2444,plain,
    ( equalish(e_1,e_3)
    | ~ product(e_1,e_1,e_3) ),
    inference(resolution,[status(thm)],[c_2440,c_2131]) ).

tff(c_2491,plain,
    ~ product(e_1,e_1,e_3),
    inference(negUnitSimplification,[status(thm)],[c_18,c_2444]) ).

tff(c_2534,plain,
    ( product(e_1,e_1,e_2)
    | product(e_1,e_1,e_1)
    | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_28,c_2491]) ).

tff(c_2537,plain,
    ( product(e_1,e_1,e_2)
    | product(e_1,e_1,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_10,c_2534]) ).

tff(c_3651,plain,
    product(e_1,e_1,e_1),
    inference(splitLeft,[status(thm)],[c_2537]) ).

tff(c_3194,plain,
    ! [X_149] :
      ( ~ product(X_149,e_3,e_1)
      | product(X_149,e_2,e_3) ),
    inference(resolution,[status(thm)],[c_1592,c_6]) ).

tff(c_3217,plain,
    ( product(e_3,e_2,e_3)
    | product(e_2,e_3,e_1)
    | product(e_1,e_3,e_1)
    | ~ group_element(e_1)
    | ~ group_element(e_3) ),
    inference(resolution,[status(thm)],[c_2,c_3194]) ).

tff(c_3228,plain,
    ( product(e_3,e_2,e_3)
    | product(e_2,e_3,e_1)
    | product(e_1,e_3,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_10,c_3217]) ).

tff(c_3229,plain,
    ( product(e_2,e_3,e_1)
    | product(e_1,e_3,e_1) ),
    inference(negUnitSimplification,[status(thm)],[c_1302,c_3228]) ).

tff(c_3231,plain,
    product(e_1,e_3,e_1),
    inference(splitLeft,[status(thm)],[c_3229]) ).

tff(c_3319,plain,
    ! [W_20] :
      ( equalish(W_20,e_3)
      | ~ product(e_1,W_20,e_1) ),
    inference(resolution,[status(thm)],[c_3231,c_32]) ).

tff(c_3654,plain,
    equalish(e_1,e_3),
    inference(resolution,[status(thm)],[c_3651,c_3319]) ).

tff(c_3682,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_18,c_3654]) ).

tff(c_3684,plain,
    ~ product(e_1,e_1,e_1),
    inference(splitRight,[status(thm)],[c_2537]) ).

tff(c_3685,plain,
    ! [X_154] :
      ( product(X_154,e_1,e_1)
      | ~ product(X_154,e_3,e_1) ),
    inference(resolution,[status(thm)],[c_3231,c_36]) ).

tff(c_3692,plain,
    product(e_1,e_1,e_1),
    inference(resolution,[status(thm)],[c_3231,c_3685]) ).

tff(c_3722,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3684,c_3692]) ).

tff(c_3724,plain,
    ~ product(e_1,e_3,e_1),
    inference(splitRight,[status(thm)],[c_3229]) ).

tff(c_3727,plain,
    ~ product(e_1,e_2,e_3),
    inference(resolution,[status(thm)],[c_1654,c_3724]) ).

tff(c_3734,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2062,c_3727]) ).

tff(c_3735,plain,
    product(e_2,e_2,e_3),
    inference(splitRight,[status(thm)],[c_1591]) ).

tff(c_4147,plain,
    ! [X_160] :
      ( ~ product(X_160,e_2,e_3)
      | product(X_160,e_2,e_2) ),
    inference(resolution,[status(thm)],[c_3735,c_6]) ).

tff(c_4187,plain,
    product(e_2,e_2,e_2),
    inference(resolution,[status(thm)],[c_3735,c_4147]) ).

tff(c_3805,plain,
    ! [W_17] :
      ( equalish(W_17,e_3)
      | ~ product(e_2,e_2,W_17) ),
    inference(resolution,[status(thm)],[c_3735,c_30]) ).

tff(c_4207,plain,
    equalish(e_2,e_3),
    inference(resolution,[status(thm)],[c_4187,c_3805]) ).

tff(c_4235,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_22,c_4207]) ).

tff(c_4236,plain,
    product(e_3,e_2,e_2),
    inference(splitRight,[status(thm)],[c_1588]) ).

tff(c_8,plain,
    ! [X_12,Y_10,Z1_9,Z2_11] :
      ( ~ product(X_12,Y_10,Z1_9)
      | ~ product(X_12,Z1_9,Z2_11)
      | product(Z1_9,Y_10,Z2_11) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_6343,plain,
    ! [Z2_185] :
      ( ~ product(e_3,e_2,Z2_185)
      | product(e_2,e_2,Z2_185) ),
    inference(resolution,[status(thm)],[c_4236,c_8]) ).

tff(c_6381,plain,
    product(e_2,e_2,e_2),
    inference(resolution,[status(thm)],[c_4236,c_6343]) ).

tff(c_20,plain,
    ~ equalish(e_2,e_1),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_5681,plain,
    ! [Z2_178] :
      ( ~ product(e_3,e_2,Z2_178)
      | product(e_2,e_2,Z2_178) ),
    inference(resolution,[status(thm)],[c_4236,c_8]) ).

tff(c_5719,plain,
    product(e_2,e_2,e_2),
    inference(resolution,[status(thm)],[c_4236,c_5681]) ).

tff(c_4237,plain,
    ~ product(e_3,e_2,e_1),
    inference(splitRight,[status(thm)],[c_1588]) ).

tff(c_4601,plain,
    ( product(e_2,e_2,e_1)
    | product(e_1,e_2,e_1)
    | ~ group_element(e_1)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_2,c_4237]) ).

tff(c_4610,plain,
    ( product(e_2,e_2,e_1)
    | product(e_1,e_2,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_10,c_4601]) ).

tff(c_5226,plain,
    product(e_1,e_2,e_1),
    inference(splitLeft,[status(thm)],[c_4610]) ).

tff(c_4938,plain,
    product(e_1,e_2,e_3),
    inference(splitLeft,[status(thm)],[c_1591]) ).

tff(c_5008,plain,
    ! [W_17] :
      ( equalish(W_17,e_3)
      | ~ product(e_1,e_2,W_17) ),
    inference(resolution,[status(thm)],[c_4938,c_30]) ).

tff(c_5417,plain,
    equalish(e_1,e_3),
    inference(resolution,[status(thm)],[c_5226,c_5008]) ).

tff(c_5445,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_18,c_5417]) ).

tff(c_5446,plain,
    product(e_2,e_2,e_1),
    inference(splitRight,[status(thm)],[c_4610]) ).

tff(c_5497,plain,
    ! [W_17] :
      ( equalish(W_17,e_1)
      | ~ product(e_2,e_2,W_17) ),
    inference(resolution,[status(thm)],[c_5446,c_30]) ).

tff(c_5994,plain,
    equalish(e_2,e_1),
    inference(resolution,[status(thm)],[c_5719,c_5497]) ).

tff(c_6025,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_20,c_5994]) ).

tff(c_6026,plain,
    product(e_2,e_2,e_3),
    inference(splitRight,[status(thm)],[c_1591]) ).

tff(c_6097,plain,
    ! [W_17] :
      ( equalish(W_17,e_3)
      | ~ product(e_2,e_2,W_17) ),
    inference(resolution,[status(thm)],[c_6026,c_30]) ).

tff(c_6401,plain,
    equalish(e_2,e_3),
    inference(resolution,[status(thm)],[c_6381,c_6097]) ).

tff(c_6432,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_22,c_6401]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRP128-4.003 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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
% 0.12/0.34  % Computer : n017.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu Aug  3 21:53:51 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 7.14/2.65  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.14/2.66  
% 7.14/2.66  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.33/2.71  
% 7.33/2.71  Inference rules
% 7.33/2.71  ----------------------
% 7.33/2.71  #Ref     : 0
% 7.33/2.71  #Sup     : 1241
% 7.33/2.71  #Fact    : 6
% 7.33/2.71  #Define  : 0
% 7.33/2.71  #Split   : 8
% 7.33/2.71  #Chain   : 0
% 7.33/2.71  #Close   : 0
% 7.33/2.71  
% 7.33/2.71  Ordering : KBO
% 7.33/2.71  
% 7.33/2.71  Simplification rules
% 7.33/2.71  ----------------------
% 7.33/2.71  #Subsume      : 56
% 7.33/2.71  #Demod        : 1113
% 7.33/2.71  #Tautology    : 218
% 7.33/2.71  #SimpNegUnit  : 159
% 7.33/2.71  #BackRed      : 0
% 7.33/2.71  
% 7.33/2.71  #Partial instantiations: 0
% 7.33/2.71  #Strategies tried      : 1
% 7.33/2.71  
% 7.33/2.71  Timing (in seconds)
% 7.33/2.71  ----------------------
% 7.33/2.71  Preprocessing        : 0.44
% 7.33/2.71  Parsing              : 0.24
% 7.33/2.71  CNF conversion       : 0.02
% 7.33/2.71  Main loop            : 1.20
% 7.33/2.71  Inferencing          : 0.38
% 7.33/2.71  Reduction            : 0.31
% 7.33/2.71  Demodulation         : 0.19
% 7.33/2.71  BG Simplification    : 0.05
% 7.33/2.71  Subsumption          : 0.40
% 7.33/2.71  Abstraction          : 0.04
% 7.33/2.71  MUC search           : 0.00
% 7.33/2.71  Cooper               : 0.00
% 7.33/2.71  Total                : 1.72
% 7.33/2.71  Index Insertion      : 0.00
% 7.33/2.71  Index Deletion       : 0.00
% 7.33/2.71  Index Matching       : 0.00
% 7.33/2.71  BG Taut test         : 0.00
%------------------------------------------------------------------------------