TSTP Solution File: PUZ021-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : PUZ021-1 : 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/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 : n001.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 10:54:01 EDT 2023

% Result   : Unsatisfiable 4.47s 2.19s
% Output   : CNFRefutation 4.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   84 (  23 unt;   8 typ;   0 def)
%            Number of atoms       :  147 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  134 (  63   ~;  71   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (   7   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-2 aty)
%            Number of variables   :  120 (; 120   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ says > a_truth > and > #nlpp > rich > poor > knight > knave > me

%Foreground sorts:

%Background operators:

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

tff(knave,type,
    knave: $i > $i ).

tff(knight,type,
    knight: $i > $i ).

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

tff(poor,type,
    poor: $i > $i ).

tff(and,type,
    and: ( $i * $i ) > $i ).

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

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

tff(f_42,axiom,
    ! [X,Y] :
      ( a_truth(knight(X),Y)
      | a_truth(knave(X),Y) ),
    file(unknown,unknown) ).

tff(f_112,axiom,
    ! [X] :
      ( says(me,X)
      | a_truth(and(knave(me),rich(me)),X) ),
    file(unknown,unknown) ).

tff(f_89,axiom,
    ! [X,Y,Z] :
      ( ~ a_truth(and(X,Y),Z)
      | a_truth(X,Z) ),
    file(unknown,unknown) ).

tff(f_84,axiom,
    ! [X,Z,Y] :
      ( ~ a_truth(knave(X),Z)
      | says(X,Y)
      | a_truth(Y,Z) ),
    file(unknown,unknown) ).

tff(f_94,axiom,
    ! [X,Y,Z] :
      ( ~ a_truth(and(X,Y),Z)
      | a_truth(Y,Z) ),
    file(unknown,unknown) ).

tff(f_48,axiom,
    ! [X,Y] :
      ( ~ a_truth(rich(X),Y)
      | ~ a_truth(poor(X),Y) ),
    file(unknown,unknown) ).

tff(f_60,axiom,
    ! [X,Z,Y] :
      ( ~ a_truth(knight(X),Z)
      | ~ says(X,Y)
      | a_truth(Y,Z) ),
    file(unknown,unknown) ).

tff(f_102,axiom,
    ! [X,Y,Z] :
      ( a_truth(and(X,Y),Z)
      | ~ a_truth(X,Z)
      | ~ a_truth(Y,Z) ),
    file(unknown,unknown) ).

tff(f_108,axiom,
    ! [X] :
      ( ~ says(me,X)
      | ~ a_truth(and(knave(me),rich(me)),X) ),
    file(unknown,unknown) ).

tff(f_52,axiom,
    ! [X,Y] :
      ( a_truth(rich(X),Y)
      | a_truth(poor(X),Y) ),
    file(unknown,unknown) ).

tff(f_77,axiom,
    ! [X,Z,Y] :
      ( ~ a_truth(knave(X),Z)
      | ~ says(X,Y)
      | ~ a_truth(Y,Z) ),
    file(unknown,unknown) ).

tff(c_4,plain,
    ! [X_3,Y_4] :
      ( a_truth(knave(X_3),Y_4)
      | a_truth(knight(X_3),Y_4) ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_56,plain,
    ! [X_55] :
      ( a_truth(and(knave(me),rich(me)),X_55)
      | says(me,X_55) ),
    inference(cnfTransformation,[status(thm)],[f_112]) ).

tff(c_18,plain,
    ! [X_21,Z_23,Y_22] :
      ( a_truth(X_21,Z_23)
      | ~ a_truth(and(X_21,Y_22),Z_23) ),
    inference(cnfTransformation,[status(thm)],[f_89]) ).

tff(c_69,plain,
    ! [X_55] :
      ( a_truth(knave(me),X_55)
      | says(me,X_55) ),
    inference(resolution,[status(thm)],[c_56,c_18]) ).

tff(c_95,plain,
    ! [Y_60,Z_61,X_62] :
      ( a_truth(Y_60,Z_61)
      | says(X_62,Y_60)
      | ~ a_truth(knave(X_62),Z_61) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_98,plain,
    ! [Y_60,X_55] :
      ( a_truth(Y_60,X_55)
      | says(me,Y_60)
      | says(me,X_55) ),
    inference(resolution,[status(thm)],[c_69,c_95]) ).

tff(c_180,plain,
    ! [Y_68] :
      ( a_truth(Y_68,Y_68)
      | says(me,Y_68) ),
    inference(factorization,[status(thm),theory(equality)],[c_98]) ).

tff(c_370,plain,
    ! [X_80,Y_81] :
      ( a_truth(X_80,and(X_80,Y_81))
      | says(me,and(X_80,Y_81)) ),
    inference(resolution,[status(thm)],[c_180,c_18]) ).

tff(c_20,plain,
    ! [Y_25,Z_26,X_24] :
      ( a_truth(Y_25,Z_26)
      | ~ a_truth(and(X_24,Y_25),Z_26) ),
    inference(cnfTransformation,[status(thm)],[f_94]) ).

tff(c_78,plain,
    ! [X_57] :
      ( a_truth(rich(me),X_57)
      | says(me,X_57) ),
    inference(resolution,[status(thm)],[c_56,c_20]) ).

tff(c_6,plain,
    ! [X_5,Y_6] :
      ( ~ a_truth(poor(X_5),Y_6)
      | ~ a_truth(rich(X_5),Y_6) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_88,plain,
    ! [X_57] :
      ( ~ a_truth(poor(me),X_57)
      | says(me,X_57) ),
    inference(resolution,[status(thm)],[c_78,c_6]) ).

tff(c_424,plain,
    ! [Y_82] : says(me,and(poor(me),Y_82)),
    inference(resolution,[status(thm)],[c_370,c_88]) ).

tff(c_10,plain,
    ! [Y_11,Z_10,X_9] :
      ( a_truth(Y_11,Z_10)
      | ~ says(X_9,Y_11)
      | ~ a_truth(knight(X_9),Z_10) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_1571,plain,
    ! [Y_125,Z_126] :
      ( a_truth(and(poor(me),Y_125),Z_126)
      | ~ a_truth(knight(me),Z_126) ),
    inference(resolution,[status(thm)],[c_424,c_10]) ).

tff(c_1586,plain,
    ! [Y_127,Z_128] :
      ( a_truth(Y_127,Z_128)
      | ~ a_truth(knight(me),Z_128) ),
    inference(resolution,[status(thm)],[c_1571,c_20]) ).

tff(c_1636,plain,
    ! [Y_127,Y_4] :
      ( a_truth(Y_127,Y_4)
      | a_truth(knave(me),Y_4) ),
    inference(resolution,[status(thm)],[c_4,c_1586]) ).

tff(c_1648,plain,
    ! [Y_4] : a_truth(knave(me),Y_4),
    inference(factorization,[status(thm),theory(equality)],[c_1636]) ).

tff(c_1787,plain,
    ! [Y_131] : a_truth(knave(me),Y_131),
    inference(factorization,[status(thm),theory(equality)],[c_1636]) ).

tff(c_16,plain,
    ! [Y_20,Z_19,X_18] :
      ( a_truth(Y_20,Z_19)
      | says(X_18,Y_20)
      | ~ a_truth(knave(X_18),Z_19) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_1815,plain,
    ! [Y_20,Y_131] :
      ( a_truth(Y_20,Y_131)
      | says(me,Y_20) ),
    inference(resolution,[status(thm)],[c_1787,c_16]) ).

tff(c_99,plain,
    ! [Y_63,Z_64,X_65] :
      ( ~ a_truth(Y_63,Z_64)
      | ~ a_truth(X_65,Z_64)
      | a_truth(and(X_65,Y_63),Z_64) ),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_24,plain,
    ! [X_30] :
      ( ~ a_truth(and(knave(me),rich(me)),X_30)
      | ~ says(me,X_30) ),
    inference(cnfTransformation,[status(thm)],[f_108]) ).

tff(c_114,plain,
    ! [Z_64] :
      ( ~ says(me,Z_64)
      | ~ a_truth(rich(me),Z_64)
      | ~ a_truth(knave(me),Z_64) ),
    inference(resolution,[status(thm)],[c_99,c_24]) ).

tff(c_1978,plain,
    ! [Z_136] :
      ( ~ says(me,Z_136)
      | ~ a_truth(rich(me),Z_136) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1648,c_114]) ).

tff(c_1998,plain,
    ! [Y_131] :
      ( ~ says(me,Y_131)
      | says(me,rich(me)) ),
    inference(resolution,[status(thm)],[c_1815,c_1978]) ).

tff(c_2025,plain,
    ! [Y_131] : ~ says(me,Y_131),
    inference(splitLeft,[status(thm)],[c_1998]) ).

tff(c_216,plain,
    says(me,poor(me)),
    inference(resolution,[status(thm)],[c_180,c_88]) ).

tff(c_227,plain,
    ! [Z_69] :
      ( a_truth(poor(me),Z_69)
      | ~ a_truth(knight(me),Z_69) ),
    inference(resolution,[status(thm)],[c_216,c_10]) ).

tff(c_235,plain,
    ! [Z_69] :
      ( says(me,Z_69)
      | ~ a_truth(knight(me),Z_69) ),
    inference(resolution,[status(thm)],[c_227,c_88]) ).

tff(c_413,plain,
    ! [Y_81] : says(me,and(knight(me),Y_81)),
    inference(resolution,[status(thm)],[c_370,c_235]) ).

tff(c_2056,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2025,c_413]) ).

tff(c_2057,plain,
    says(me,rich(me)),
    inference(splitRight,[status(thm)],[c_1998]) ).

tff(c_8,plain,
    ! [X_7,Y_8] :
      ( a_truth(poor(X_7),Y_8)
      | a_truth(rich(X_7),Y_8) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_49,plain,
    ! [Y_52,Z_53,X_54] :
      ( ~ a_truth(Y_52,Z_53)
      | ~ says(X_54,Y_52)
      | ~ a_truth(knave(X_54),Z_53) ),
    inference(cnfTransformation,[status(thm)],[f_77]) ).

tff(c_55,plain,
    ! [X_54,X_7,Y_8] :
      ( ~ says(X_54,rich(X_7))
      | ~ a_truth(knave(X_54),Y_8)
      | a_truth(poor(X_7),Y_8) ),
    inference(resolution,[status(thm)],[c_8,c_49]) ).

tff(c_2059,plain,
    ! [Y_8] :
      ( ~ a_truth(knave(me),Y_8)
      | a_truth(poor(me),Y_8) ),
    inference(resolution,[status(thm)],[c_2057,c_55]) ).

tff(c_2064,plain,
    ! [Y_8] : a_truth(poor(me),Y_8),
    inference(demodulation,[status(thm),theory(equality)],[c_1648,c_2059]) ).

tff(c_2068,plain,
    ! [X_57] : says(me,X_57),
    inference(demodulation,[status(thm),theory(equality)],[c_2064,c_88]) ).

tff(c_500,plain,
    ! [Y_90,Z_91] :
      ( a_truth(Y_90,Z_91)
      | ~ a_truth(knight(me),Z_91)
      | a_truth(Y_90,Y_90) ),
    inference(resolution,[status(thm)],[c_180,c_10]) ).

tff(c_524,plain,
    ! [Y_90,Y_4] :
      ( a_truth(Y_90,Y_4)
      | a_truth(Y_90,Y_90)
      | a_truth(knave(me),Y_4) ),
    inference(resolution,[status(thm)],[c_4,c_500]) ).

tff(c_676,plain,
    a_truth(knave(me),knave(me)),
    inference(factorization,[status(thm),theory(equality)],[c_524]) ).

tff(c_997,plain,
    ! [Y_105] :
      ( a_truth(Y_105,knave(me))
      | says(me,Y_105) ),
    inference(resolution,[status(thm)],[c_676,c_16]) ).

tff(c_1015,plain,
    ( ~ says(me,knave(me))
    | ~ a_truth(knave(me),knave(me))
    | says(me,rich(me)) ),
    inference(resolution,[status(thm)],[c_997,c_114]) ).

tff(c_1058,plain,
    ( ~ says(me,knave(me))
    | says(me,rich(me)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_676,c_1015]) ).

tff(c_1071,plain,
    ~ says(me,knave(me)),
    inference(splitLeft,[status(thm)],[c_1058]) ).

tff(c_2124,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2068,c_1071]) ).

tff(c_2126,plain,
    says(me,knave(me)),
    inference(splitRight,[status(thm)],[c_1058]) ).

tff(c_2188,plain,
    ! [Z_143] :
      ( a_truth(knave(me),Z_143)
      | ~ a_truth(knight(me),Z_143) ),
    inference(resolution,[status(thm)],[c_2126,c_10]) ).

tff(c_2238,plain,
    ! [Y_4] : a_truth(knave(me),Y_4),
    inference(resolution,[status(thm)],[c_4,c_2188]) ).

tff(c_2125,plain,
    says(me,rich(me)),
    inference(splitRight,[status(thm)],[c_1058]) ).

tff(c_2417,plain,
    ! [X_149,X_150,Y_151] :
      ( ~ says(X_149,rich(X_150))
      | ~ a_truth(knave(X_149),Y_151)
      | a_truth(poor(X_150),Y_151) ),
    inference(resolution,[status(thm)],[c_8,c_49]) ).

tff(c_2422,plain,
    ! [Y_151] :
      ( ~ a_truth(knave(me),Y_151)
      | a_truth(poor(me),Y_151) ),
    inference(resolution,[status(thm)],[c_2125,c_2417]) ).

tff(c_2436,plain,
    ! [Y_151] : a_truth(poor(me),Y_151),
    inference(demodulation,[status(thm),theory(equality)],[c_2238,c_2422]) ).

tff(c_2446,plain,
    ! [X_57] : says(me,X_57),
    inference(demodulation,[status(thm),theory(equality)],[c_2436,c_88]) ).

tff(c_2490,plain,
    ! [X_153] : says(me,X_153),
    inference(demodulation,[status(thm),theory(equality)],[c_2436,c_88]) ).

tff(c_2493,plain,
    ! [Y_8,X_7] :
      ( ~ a_truth(knave(me),Y_8)
      | a_truth(poor(X_7),Y_8) ),
    inference(resolution,[status(thm)],[c_2490,c_55]) ).

tff(c_2501,plain,
    ! [X_7,Y_8] : a_truth(poor(X_7),Y_8),
    inference(demodulation,[status(thm),theory(equality)],[c_2238,c_2493]) ).

tff(c_54,plain,
    ! [X_54,X_3,Y_4] :
      ( ~ says(X_54,knight(X_3))
      | ~ a_truth(knave(X_54),Y_4)
      | a_truth(knave(X_3),Y_4) ),
    inference(resolution,[status(thm)],[c_4,c_49]) ).

tff(c_2496,plain,
    ! [Y_4,X_3] :
      ( ~ a_truth(knave(me),Y_4)
      | a_truth(knave(X_3),Y_4) ),
    inference(resolution,[status(thm)],[c_2490,c_54]) ).

tff(c_2504,plain,
    ! [X_3,Y_4] : a_truth(knave(X_3),Y_4),
    inference(demodulation,[status(thm),theory(equality)],[c_2238,c_2496]) ).

tff(c_14,plain,
    ! [Y_17,Z_16,X_15] :
      ( ~ a_truth(Y_17,Z_16)
      | ~ says(X_15,Y_17)
      | ~ a_truth(knave(X_15),Z_16) ),
    inference(cnfTransformation,[status(thm)],[f_77]) ).

tff(c_2559,plain,
    ! [Y_165,Z_166,X_167] :
      ( ~ a_truth(Y_165,Z_166)
      | ~ says(X_167,Y_165) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2504,c_14]) ).

tff(c_2569,plain,
    ! [X_168,X_169] : ~ says(X_168,poor(X_169)),
    inference(resolution,[status(thm)],[c_2501,c_2559]) ).

tff(c_2574,plain,
    $false,
    inference(resolution,[status(thm)],[c_2446,c_2569]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : PUZ021-1 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.15  % 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
% 0.14/0.37  % Computer : n001.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit : 300
% 0.14/0.37  % WCLimit  : 300
% 0.14/0.37  % DateTime : Thu Aug  3 18:08:25 EDT 2023
% 0.14/0.38  % CPUTime  : 
% 4.47/2.19  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.47/2.20  
% 4.47/2.20  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.47/2.26  
% 4.47/2.26  Inference rules
% 4.47/2.26  ----------------------
% 4.47/2.26  #Ref     : 0
% 4.47/2.26  #Sup     : 484
% 4.47/2.27  #Fact    : 22
% 4.47/2.27  #Define  : 0
% 4.47/2.27  #Split   : 2
% 4.47/2.27  #Chain   : 0
% 4.47/2.27  #Close   : 0
% 4.47/2.27  
% 4.47/2.27  Ordering : KBO
% 4.47/2.27  
% 4.47/2.27  Simplification rules
% 4.47/2.27  ----------------------
% 4.47/2.27  #Subsume      : 119
% 4.47/2.27  #Demod        : 205
% 4.47/2.27  #Tautology    : 193
% 4.47/2.27  #SimpNegUnit  : 49
% 4.47/2.27  #BackRed      : 46
% 4.47/2.27  
% 4.47/2.27  #Partial instantiations: 0
% 4.47/2.27  #Strategies tried      : 1
% 4.47/2.27  
% 4.47/2.27  Timing (in seconds)
% 4.47/2.27  ----------------------
% 4.47/2.27  Preprocessing        : 0.44
% 4.47/2.27  Parsing              : 0.24
% 4.47/2.27  CNF conversion       : 0.03
% 4.47/2.27  Main loop            : 0.73
% 4.47/2.27  Inferencing          : 0.30
% 4.47/2.27  Reduction            : 0.15
% 4.47/2.27  Demodulation         : 0.10
% 4.47/2.27  BG Simplification    : 0.03
% 4.47/2.27  Subsumption          : 0.18
% 4.47/2.27  Abstraction          : 0.03
% 4.47/2.27  MUC search           : 0.00
% 4.47/2.27  Cooper               : 0.00
% 4.47/2.27  Total                : 1.25
% 4.47/2.27  Index Insertion      : 0.00
% 4.47/2.27  Index Deletion       : 0.00
% 4.47/2.27  Index Matching       : 0.00
% 4.47/2.27  BG Taut test         : 0.00
%------------------------------------------------------------------------------