TSTP Solution File: GRP123-6.003 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP123-6.003 : 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/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 : n029.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 10:39:54 EDT 2023

% Result   : Unsatisfiable 4.71s 2.06s
% Output   : CNFRefutation 4.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   69 (  27 unt;   7 typ;   0 def)
%            Number of atoms       :  145 (   0 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  149 (  66   ~;  83   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   4   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   77 (;  77   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ product2 > product1 > 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(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_34,axiom,
    ~ equalish(e_1,e_2),
    file(unknown,unknown) ).

tff(f_36,axiom,
    ~ equalish(e_1,e_3),
    file(unknown,unknown) ).

tff(f_30,axiom,
    group_element(e_1),
    file(unknown,unknown) ).

tff(f_32,axiom,
    group_element(e_3),
    file(unknown,unknown) ).

tff(f_56,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_82,axiom,
    ! [X] : product1(X,X,X),
    file(unknown,unknown) ).

tff(f_80,axiom,
    ! [W,Y,X,Z] :
      ( ~ product1(W,Y,X)
      | ~ product1(Z,Y,X)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(f_42,axiom,
    ~ equalish(e_3,e_1),
    file(unknown,unknown) ).

tff(f_38,axiom,
    ~ equalish(e_2,e_1),
    file(unknown,unknown) ).

tff(f_40,axiom,
    ~ equalish(e_2,e_3),
    file(unknown,unknown) ).

tff(f_44,axiom,
    ~ equalish(e_3,e_2),
    file(unknown,unknown) ).

tff(f_31,axiom,
    group_element(e_2),
    file(unknown,unknown) ).

tff(f_72,axiom,
    ! [X,W,Y,Z] :
      ( ~ product1(X,W,Y)
      | ~ product1(X,Z,Y)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(f_128,axiom,
    ! [X,Y,Z1,Z2] :
      ( ~ product1(X,Y,Z1)
      | ~ product1(Z1,Y,Z2)
      | product2(Z2,X,Y) ),
    file(unknown,unknown) ).

tff(f_94,axiom,
    ! [X,Y] :
      ( ~ group_element(X)
      | ~ group_element(Y)
      | product2(X,Y,e_1)
      | product2(X,Y,e_2)
      | product2(X,Y,e_3) ),
    file(unknown,unknown) ).

tff(f_120,axiom,
    ! [X] : product2(X,X,X),
    file(unknown,unknown) ).

tff(f_102,axiom,
    ! [X,Y,W,Z] :
      ( ~ product2(X,Y,W)
      | ~ product2(X,Y,Z)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(c_8,plain,
    ~ equalish(e_1,e_2),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_10,plain,
    ~ equalish(e_1,e_3),
    inference(cnfTransformation,[status(thm)],[f_36]) ).

tff(c_2,plain,
    group_element(e_1),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_6,plain,
    group_element(e_3),
    inference(cnfTransformation,[status(thm)],[f_32]) ).

tff(c_190,plain,
    ! [X_88,Y_89] :
      ( product1(X_88,Y_89,e_3)
      | product1(X_88,Y_89,e_2)
      | product1(X_88,Y_89,e_1)
      | ~ group_element(Y_89)
      | ~ group_element(X_88) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_28,plain,
    ! [X_15] : product1(X_15,X_15,X_15),
    inference(cnfTransformation,[status(thm)],[f_82]) ).

tff(c_73,plain,
    ! [W_56,Z_57,Y_58,X_59] :
      ( equalish(W_56,Z_57)
      | ~ product1(Z_57,Y_58,X_59)
      | ~ product1(W_56,Y_58,X_59) ),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_76,plain,
    ! [W_56,X_15] :
      ( equalish(W_56,X_15)
      | ~ product1(W_56,X_15,X_15) ),
    inference(resolution,[status(thm)],[c_28,c_73]) ).

tff(c_202,plain,
    ! [X_88] :
      ( equalish(X_88,e_3)
      | product1(X_88,e_3,e_2)
      | product1(X_88,e_3,e_1)
      | ~ group_element(e_3)
      | ~ group_element(X_88) ),
    inference(resolution,[status(thm)],[c_190,c_76]) ).

tff(c_216,plain,
    ! [X_88] :
      ( equalish(X_88,e_3)
      | product1(X_88,e_3,e_2)
      | product1(X_88,e_3,e_1)
      | ~ group_element(X_88) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_202]) ).

tff(c_16,plain,
    ~ equalish(e_3,e_1),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_12,plain,
    ~ equalish(e_2,e_1),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_14,plain,
    ~ equalish(e_2,e_3),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_18,plain,
    ~ equalish(e_3,e_2),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_4,plain,
    group_element(e_2),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_756,plain,
    ! [X_119] :
      ( equalish(X_119,e_3)
      | product1(X_119,e_3,e_2)
      | product1(X_119,e_3,e_1)
      | ~ group_element(X_119) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_202]) ).

tff(c_53,plain,
    ! [W_44,Z_45,X_46,Y_47] :
      ( equalish(W_44,Z_45)
      | ~ product1(X_46,Z_45,Y_47)
      | ~ product1(X_46,W_44,Y_47) ),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_56,plain,
    ! [W_44,X_15] :
      ( equalish(W_44,X_15)
      | ~ product1(X_15,W_44,X_15) ),
    inference(resolution,[status(thm)],[c_28,c_53]) ).

tff(c_772,plain,
    ( equalish(e_3,e_2)
    | equalish(e_2,e_3)
    | product1(e_2,e_3,e_1)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_756,c_56]) ).

tff(c_788,plain,
    ( equalish(e_3,e_2)
    | equalish(e_2,e_3)
    | product1(e_2,e_3,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_772]) ).

tff(c_789,plain,
    product1(e_2,e_3,e_1),
    inference(negUnitSimplification,[status(thm)],[c_14,c_18,c_788]) ).

tff(c_40,plain,
    ! [Z2_34,X_31,Y_32,Z1_33] :
      ( product2(Z2_34,X_31,Y_32)
      | ~ product1(Z1_33,Y_32,Z2_34)
      | ~ product1(X_31,Y_32,Z1_33) ),
    inference(cnfTransformation,[status(thm)],[f_128]) ).

tff(c_875,plain,
    ! [X_123] :
      ( product2(e_1,X_123,e_3)
      | ~ product1(X_123,e_3,e_2) ),
    inference(resolution,[status(thm)],[c_789,c_40]) ).

tff(c_107,plain,
    ! [X_78,Y_79] :
      ( product2(X_78,Y_79,e_3)
      | product2(X_78,Y_79,e_2)
      | product2(X_78,Y_79,e_1)
      | ~ group_element(Y_79)
      | ~ group_element(X_78) ),
    inference(cnfTransformation,[status(thm)],[f_94]) ).

tff(c_38,plain,
    ! [X_30] : product2(X_30,X_30,X_30),
    inference(cnfTransformation,[status(thm)],[f_120]) ).

tff(c_77,plain,
    ! [W_60,Z_61,X_62,Y_63] :
      ( equalish(W_60,Z_61)
      | ~ product2(X_62,Y_63,Z_61)
      | ~ product2(X_62,Y_63,W_60) ),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_80,plain,
    ! [W_60,X_30] :
      ( equalish(W_60,X_30)
      | ~ product2(X_30,X_30,W_60) ),
    inference(resolution,[status(thm)],[c_38,c_77]) ).

tff(c_248,plain,
    ! [Y_95] :
      ( equalish(e_3,Y_95)
      | product2(Y_95,Y_95,e_2)
      | product2(Y_95,Y_95,e_1)
      | ~ group_element(Y_95) ),
    inference(resolution,[status(thm)],[c_107,c_80]) ).

tff(c_103,plain,
    ! [Z2_74,X_75,Y_76,Z1_77] :
      ( product2(Z2_74,X_75,Y_76)
      | ~ product1(Z1_77,Y_76,Z2_74)
      | ~ product1(X_75,Y_76,Z1_77) ),
    inference(cnfTransformation,[status(thm)],[f_128]) ).

tff(c_136,plain,
    ! [X_80,X_81] :
      ( product2(X_80,X_81,X_80)
      | ~ product1(X_81,X_80,X_80) ),
    inference(resolution,[status(thm)],[c_28,c_103]) ).

tff(c_32,plain,
    ! [W_20,Z_21,X_18,Y_19] :
      ( equalish(W_20,Z_21)
      | ~ product2(X_18,Y_19,Z_21)
      | ~ product2(X_18,Y_19,W_20) ),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_157,plain,
    ! [W_20,X_80,X_81] :
      ( equalish(W_20,X_80)
      | ~ product2(X_80,X_81,W_20)
      | ~ product1(X_81,X_80,X_80) ),
    inference(resolution,[status(thm)],[c_136,c_32]) ).

tff(c_255,plain,
    ! [Y_95] :
      ( equalish(e_2,Y_95)
      | ~ product1(Y_95,Y_95,Y_95)
      | equalish(e_3,Y_95)
      | product2(Y_95,Y_95,e_1)
      | ~ group_element(Y_95) ),
    inference(resolution,[status(thm)],[c_248,c_157]) ).

tff(c_293,plain,
    ! [Y_96] :
      ( equalish(e_2,Y_96)
      | equalish(e_3,Y_96)
      | product2(Y_96,Y_96,e_1)
      | ~ group_element(Y_96) ),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_255]) ).

tff(c_327,plain,
    ! [W_20,Y_96] :
      ( equalish(W_20,e_1)
      | ~ product2(Y_96,Y_96,W_20)
      | equalish(e_2,Y_96)
      | equalish(e_3,Y_96)
      | ~ group_element(Y_96) ),
    inference(resolution,[status(thm)],[c_293,c_32]) ).

tff(c_879,plain,
    ( equalish(e_2,e_1)
    | equalish(e_3,e_1)
    | ~ group_element(e_1)
    | ~ product1(e_1,e_3,e_2) ),
    inference(resolution,[status(thm)],[c_875,c_327]) ).

tff(c_902,plain,
    ( equalish(e_2,e_1)
    | equalish(e_3,e_1)
    | ~ product1(e_1,e_3,e_2) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_879]) ).

tff(c_903,plain,
    ~ product1(e_1,e_3,e_2),
    inference(negUnitSimplification,[status(thm)],[c_16,c_12,c_902]) ).

tff(c_922,plain,
    ( equalish(e_1,e_3)
    | product1(e_1,e_3,e_1)
    | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_216,c_903]) ).

tff(c_925,plain,
    ( equalish(e_1,e_3)
    | product1(e_1,e_3,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_922]) ).

tff(c_926,plain,
    product1(e_1,e_3,e_1),
    inference(negUnitSimplification,[status(thm)],[c_10,c_925]) ).

tff(c_26,plain,
    ! [W_11,Z_14,Y_12,X_13] :
      ( equalish(W_11,Z_14)
      | ~ product1(Z_14,Y_12,X_13)
      | ~ product1(W_11,Y_12,X_13) ),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_807,plain,
    ! [W_11] :
      ( equalish(W_11,e_2)
      | ~ product1(W_11,e_3,e_1) ),
    inference(resolution,[status(thm)],[c_789,c_26]) ).

tff(c_957,plain,
    equalish(e_1,e_2),
    inference(resolution,[status(thm)],[c_926,c_807]) ).

tff(c_974,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_8,c_957]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : GRP123-6.003 : TPTP v8.1.2. Released v1.2.0.
% 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
% 0.17/0.35  % Computer : n029.cluster.edu
% 0.17/0.35  % Model    : x86_64 x86_64
% 0.17/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35  % Memory   : 8042.1875MB
% 0.17/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35  % CPULimit : 300
% 0.17/0.35  % WCLimit  : 300
% 0.17/0.35  % DateTime : Thu Aug  3 22:20:23 EDT 2023
% 0.17/0.35  % CPUTime  : 
% 4.71/2.06  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.71/2.07  
% 4.71/2.07  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.95/2.11  
% 4.95/2.11  Inference rules
% 4.95/2.11  ----------------------
% 4.95/2.11  #Ref     : 0
% 4.95/2.11  #Sup     : 181
% 4.95/2.11  #Fact    : 0
% 4.95/2.11  #Define  : 0
% 4.95/2.11  #Split   : 0
% 4.95/2.11  #Chain   : 0
% 4.95/2.11  #Close   : 0
% 4.95/2.11  
% 4.95/2.11  Ordering : KBO
% 4.95/2.11  
% 4.95/2.11  Simplification rules
% 4.95/2.11  ----------------------
% 4.95/2.11  #Subsume      : 21
% 4.95/2.11  #Demod        : 126
% 4.95/2.11  #Tautology    : 60
% 4.95/2.11  #SimpNegUnit  : 59
% 4.95/2.11  #BackRed      : 0
% 4.95/2.11  
% 4.95/2.11  #Partial instantiations: 0
% 4.95/2.11  #Strategies tried      : 1
% 4.95/2.11  
% 4.95/2.11  Timing (in seconds)
% 4.95/2.11  ----------------------
% 4.95/2.12  Preprocessing        : 0.45
% 4.95/2.12  Parsing              : 0.24
% 4.95/2.12  CNF conversion       : 0.03
% 4.95/2.12  Main loop            : 0.58
% 4.95/2.12  Inferencing          : 0.23
% 4.95/2.12  Reduction            : 0.15
% 4.95/2.12  Demodulation         : 0.09
% 4.95/2.12  BG Simplification    : 0.03
% 4.95/2.12  Subsumption          : 0.15
% 4.95/2.12  Abstraction          : 0.02
% 4.95/2.12  MUC search           : 0.00
% 4.95/2.12  Cooper               : 0.00
% 4.95/2.12  Total                : 1.09
% 4.95/2.12  Index Insertion      : 0.00
% 4.95/2.12  Index Deletion       : 0.00
% 4.95/2.12  Index Matching       : 0.00
% 4.95/2.12  BG Taut test         : 0.00
%------------------------------------------------------------------------------