TSTP Solution File: GRP123-7.003 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP123-7.003 : TPTP v8.1.2. Released v1.2.0.
% 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 : n005.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 10:39:55 EDT 2023

% Result   : Unsatisfiable 5.06s 2.17s
% Output   : CNFRefutation 5.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   64 (  24 unt;  10 typ;   0 def)
%            Number of atoms       :  118 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  119 (  55   ~;  64   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (   7   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   76 (;  76   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ product2 > product1 > product > next > greater > 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(greater,type,
    greater: ( $i * $i ) > $o ).

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

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

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

tff(product1,type,
    product1: ( $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(product2,type,
    product2: ( $i * $i * $i ) > $o ).

tff(f_54,axiom,
    ~ equalish(e_2,e_1),
    file(unknown,unknown) ).

tff(f_52,axiom,
    ~ equalish(e_1,e_3),
    file(unknown,unknown) ).

tff(f_46,axiom,
    group_element(e_1),
    file(unknown,unknown) ).

tff(f_47,axiom,
    group_element(e_2),
    file(unknown,unknown) ).

tff(f_72,axiom,
    ! [X,Y] :
      ( ~ group_element(X)
      | ~ group_element(Y)
      | product1(X,Y,e_1)
      | product1(X,Y,e_2)
      | product1(X,Y,e_3) ),
    file(unknown,unknown) ).

tff(f_60,axiom,
    ~ equalish(e_3,e_2),
    file(unknown,unknown) ).

tff(f_48,axiom,
    group_element(e_3),
    file(unknown,unknown) ).

tff(f_98,axiom,
    ! [X] : product1(X,X,X),
    file(unknown,unknown) ).

tff(f_88,axiom,
    ! [X,W,Y,Z] :
      ( ~ product1(X,W,Y)
      | ~ product1(X,Z,Y)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(f_96,axiom,
    ! [W,Y,X,Z] :
      ( ~ product1(W,Y,X)
      | ~ product1(Z,Y,X)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(f_144,axiom,
    ! [X,Y,Z1,Z2] :
      ( ~ product1(X,Y,Z1)
      | ~ product1(Z1,Y,Z2)
      | product2(Z2,X,Y) ),
    file(unknown,unknown) ).

tff(f_136,axiom,
    ! [X] : product2(X,X,X),
    file(unknown,unknown) ).

tff(f_118,axiom,
    ! [X,Y,W,Z] :
      ( ~ product2(X,Y,W)
      | ~ product2(X,Y,Z)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(f_126,axiom,
    ! [X,W,Y,Z] :
      ( ~ product2(X,W,Y)
      | ~ product2(X,Z,Y)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(c_24,plain,
    ~ equalish(e_2,e_1),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_22,plain,
    ~ equalish(e_1,e_3),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_14,plain,
    group_element(e_1),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_16,plain,
    group_element(e_2),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_32,plain,
    ! [X_4,Y_5] :
      ( product1(X_4,Y_5,e_3)
      | product1(X_4,Y_5,e_2)
      | product1(X_4,Y_5,e_1)
      | ~ group_element(Y_5)
      | ~ group_element(X_4) ),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_30,plain,
    ~ equalish(e_3,e_2),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_18,plain,
    group_element(e_3),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_40,plain,
    ! [X_18] : product1(X_18,X_18,X_18),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_221,plain,
    ! [X_99,Y_100] :
      ( product1(X_99,Y_100,e_3)
      | product1(X_99,Y_100,e_2)
      | product1(X_99,Y_100,e_1)
      | ~ group_element(Y_100)
      | ~ group_element(X_99) ),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_36,plain,
    ! [W_11,Z_13,X_10,Y_12] :
      ( equalish(W_11,Z_13)
      | ~ product1(X_10,Z_13,Y_12)
      | ~ product1(X_10,W_11,Y_12) ),
    inference(cnfTransformation,[status(thm)],[f_88]) ).

tff(c_333,plain,
    ! [W_105,Y_106,X_107] :
      ( equalish(W_105,Y_106)
      | ~ product1(X_107,W_105,e_3)
      | product1(X_107,Y_106,e_2)
      | product1(X_107,Y_106,e_1)
      | ~ group_element(Y_106)
      | ~ group_element(X_107) ),
    inference(resolution,[status(thm)],[c_221,c_36]) ).

tff(c_338,plain,
    ! [Y_106] :
      ( equalish(e_3,Y_106)
      | product1(e_3,Y_106,e_2)
      | product1(e_3,Y_106,e_1)
      | ~ group_element(Y_106)
      | ~ group_element(e_3) ),
    inference(resolution,[status(thm)],[c_40,c_333]) ).

tff(c_1160,plain,
    ! [Y_144] :
      ( equalish(e_3,Y_144)
      | product1(e_3,Y_144,e_2)
      | product1(e_3,Y_144,e_1)
      | ~ group_element(Y_144) ),
    inference(demodulation,[status(thm),theory(equality)],[c_18,c_338]) ).

tff(c_88,plain,
    ! [W_59,Z_60,Y_61,X_62] :
      ( equalish(W_59,Z_60)
      | ~ product1(Z_60,Y_61,X_62)
      | ~ product1(W_59,Y_61,X_62) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_91,plain,
    ! [W_59,X_18] :
      ( equalish(W_59,X_18)
      | ~ product1(W_59,X_18,X_18) ),
    inference(resolution,[status(thm)],[c_40,c_88]) ).

tff(c_1188,plain,
    ( equalish(e_3,e_2)
    | product1(e_3,e_2,e_1)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_1160,c_91]) ).

tff(c_1219,plain,
    ( equalish(e_3,e_2)
    | product1(e_3,e_2,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_1188]) ).

tff(c_1220,plain,
    product1(e_3,e_2,e_1),
    inference(negUnitSimplification,[status(thm)],[c_30,c_1219]) ).

tff(c_52,plain,
    ! [Z2_37,X_34,Y_35,Z1_36] :
      ( product2(Z2_37,X_34,Y_35)
      | ~ product1(Z1_36,Y_35,Z2_37)
      | ~ product1(X_34,Y_35,Z1_36) ),
    inference(cnfTransformation,[status(thm)],[f_144]) ).

tff(c_1314,plain,
    ! [X_151] :
      ( product2(e_1,X_151,e_2)
      | ~ product1(X_151,e_2,e_3) ),
    inference(resolution,[status(thm)],[c_1220,c_52]) ).

tff(c_50,plain,
    ! [X_33] : product2(X_33,X_33,X_33),
    inference(cnfTransformation,[status(thm)],[f_136]) ).

tff(c_98,plain,
    ! [W_65,Z_66,X_67,Y_68] :
      ( equalish(W_65,Z_66)
      | ~ product2(X_67,Y_68,Z_66)
      | ~ product2(X_67,Y_68,W_65) ),
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_101,plain,
    ! [W_65,X_33] :
      ( equalish(W_65,X_33)
      | ~ product2(X_33,X_33,W_65) ),
    inference(resolution,[status(thm)],[c_50,c_98]) ).

tff(c_1333,plain,
    ( equalish(e_2,e_1)
    | ~ product1(e_1,e_2,e_3) ),
    inference(resolution,[status(thm)],[c_1314,c_101]) ).

tff(c_1357,plain,
    ~ product1(e_1,e_2,e_3),
    inference(negUnitSimplification,[status(thm)],[c_24,c_1333]) ).

tff(c_1368,plain,
    ( product1(e_1,e_2,e_2)
    | product1(e_1,e_2,e_1)
    | ~ group_element(e_2)
    | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_32,c_1357]) ).

tff(c_1371,plain,
    ( product1(e_1,e_2,e_2)
    | product1(e_1,e_2,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_16,c_1368]) ).

tff(c_1398,plain,
    product1(e_1,e_2,e_1),
    inference(splitLeft,[status(thm)],[c_1371]) ).

tff(c_38,plain,
    ! [W_14,Z_17,Y_15,X_16] :
      ( equalish(W_14,Z_17)
      | ~ product1(Z_17,Y_15,X_16)
      | ~ product1(W_14,Y_15,X_16) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_1260,plain,
    ! [W_14] :
      ( equalish(W_14,e_3)
      | ~ product1(W_14,e_2,e_1) ),
    inference(resolution,[status(thm)],[c_1220,c_38]) ).

tff(c_1416,plain,
    equalish(e_1,e_3),
    inference(resolution,[status(thm)],[c_1398,c_1260]) ).

tff(c_1433,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_22,c_1416]) ).

tff(c_1434,plain,
    product1(e_1,e_2,e_2),
    inference(splitRight,[status(thm)],[c_1371]) ).

tff(c_128,plain,
    ! [Z2_83,X_84,Y_85,Z1_86] :
      ( product2(Z2_83,X_84,Y_85)
      | ~ product1(Z1_86,Y_85,Z2_83)
      | ~ product1(X_84,Y_85,Z1_86) ),
    inference(cnfTransformation,[status(thm)],[f_144]) ).

tff(c_132,plain,
    ! [X_87,X_88] :
      ( product2(X_87,X_88,X_87)
      | ~ product1(X_88,X_87,X_87) ),
    inference(resolution,[status(thm)],[c_40,c_128]) ).

tff(c_46,plain,
    ! [W_26,Z_28,X_25,Y_27] :
      ( equalish(W_26,Z_28)
      | ~ product2(X_25,Z_28,Y_27)
      | ~ product2(X_25,W_26,Y_27) ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_202,plain,
    ! [W_94,X_95,X_96] :
      ( equalish(W_94,X_95)
      | ~ product2(X_96,W_94,X_96)
      | ~ product1(X_95,X_96,X_96) ),
    inference(resolution,[status(thm)],[c_132,c_46]) ).

tff(c_214,plain,
    ! [X_33,X_95] :
      ( equalish(X_33,X_95)
      | ~ product1(X_95,X_33,X_33) ),
    inference(resolution,[status(thm)],[c_50,c_202]) ).

tff(c_1440,plain,
    equalish(e_2,e_1),
    inference(resolution,[status(thm)],[c_1434,c_214]) ).

tff(c_1459,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_24,c_1440]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : GRP123-7.003 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.15  % 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
% 0.19/0.36  % Computer : n005.cluster.edu
% 0.19/0.36  % Model    : x86_64 x86_64
% 0.19/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.36  % Memory   : 8042.1875MB
% 0.19/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.36  % CPULimit : 300
% 0.19/0.36  % WCLimit  : 300
% 0.19/0.36  % DateTime : Thu Aug  3 21:59:56 EDT 2023
% 0.19/0.36  % CPUTime  : 
% 5.06/2.17  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.06/2.18  
% 5.06/2.18  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.06/2.21  
% 5.06/2.21  Inference rules
% 5.06/2.21  ----------------------
% 5.06/2.21  #Ref     : 0
% 5.06/2.21  #Sup     : 267
% 5.06/2.21  #Fact    : 0
% 5.06/2.21  #Define  : 0
% 5.06/2.21  #Split   : 2
% 5.06/2.21  #Chain   : 0
% 5.06/2.21  #Close   : 0
% 5.06/2.21  
% 5.06/2.21  Ordering : KBO
% 5.06/2.21  
% 5.06/2.21  Simplification rules
% 5.06/2.21  ----------------------
% 5.06/2.21  #Subsume      : 43
% 5.06/2.21  #Demod        : 197
% 5.06/2.21  #Tautology    : 86
% 5.06/2.21  #SimpNegUnit  : 95
% 5.06/2.21  #BackRed      : 0
% 5.06/2.21  
% 5.06/2.21  #Partial instantiations: 0
% 5.06/2.21  #Strategies tried      : 1
% 5.06/2.21  
% 5.06/2.21  Timing (in seconds)
% 5.06/2.21  ----------------------
% 5.41/2.21  Preprocessing        : 0.46
% 5.41/2.21  Parsing              : 0.25
% 5.41/2.21  CNF conversion       : 0.02
% 5.41/2.21  Main loop            : 0.67
% 5.41/2.21  Inferencing          : 0.24
% 5.41/2.22  Reduction            : 0.18
% 5.41/2.22  Demodulation         : 0.12
% 5.41/2.22  BG Simplification    : 0.03
% 5.41/2.22  Subsumption          : 0.18
% 5.41/2.22  Abstraction          : 0.02
% 5.41/2.22  MUC search           : 0.00
% 5.41/2.22  Cooper               : 0.00
% 5.41/2.22  Total                : 1.18
% 5.41/2.22  Index Insertion      : 0.00
% 5.41/2.22  Index Deletion       : 0.00
% 5.41/2.22  Index Matching       : 0.00
% 5.41/2.22  BG Taut test         : 0.00
%------------------------------------------------------------------------------